So in the United States, all actions by police and the courts are governed by a system called the Burden of Proof. Each level is a general assessment of how sure you are that the accusation made is provable with all evidence collected thus far. Because evidence is specific to the nature of the charge, these various levels are nebulous when they are met, but it's a good idea to satisfy as many of the question words (Who, What, Where, Why, How?) though what can be done with each type of question. For the purposes of this discussion, imagine a gage or bar like a video game's exp bar. Empty bar is no proof of a crime at all, full bar is Beyond a Reasonable Doubt. Keep in mind that all of these are subject to the opinion of the finder of fact... until the trial starts, this will be a judge.
If we break down the initial accusation:
What: Stole complaintant's phone
Where: From his property Likely on her person or property.
Why: Vindictive bi[explative deleted] Ex-Wife*
How: During pick up of children from visitation, while complaintant was not looking. Complaintant lives alone and had no other visitors and was in home until time complaint was filed.
The last two are added by myself and not sourced from anything related to the case... we don't need to know them specifically... but for demonstration purposes we will.
So there is an accusation of a specific crime committed by a specific person who had access, opportunity, and motivation to take the phone. This rises to Reasonable Suspicion (bar is at or around 25% full, but no more than 30%) which gets you a warrant for a search. The search must look only for evidence of the crime and only in places where the evidence is likely to be located (sugar bowl rule, so named because if the warrant was issued for search related to a stolen big screen television, an officer looks inside a sugar bowl in the kitchen and finds a joint buried in the sugar, then that evidence is inadmissible because who in their right mind would believe a big screen TV would be hiding inside a closed sugar bowl. If it was impossible to hide something related to the warrant inside of an item, than you shouldn't have been looking inside of the item to begin with and the joint would not have been discovered).
When the phone is found, the burden of Proof is Now at Probable Cause (somewhere between 30% to 50% but no more). This is the Burden necessary to arrest and charge has been met. The accused must be read her Miranda Rights (which include 5th amendment right against self incrimination (remain silent), right to an attorney and to have one provided if you cannot afford one). The anything you say can and will bit is important to understand because it will never be used to exonerate you in court (per trial rules, testifying to words of another person is not allowed unless it would hurt their case. In a trial where the accused is charged with shooting at the Sheriff and the Deputy, and he tells investigators "I shot the Sheriff but I did not shoot the deputy," the investigator's testimony can only say "I shot the sheriff" because it would be detrimental to the defendant on trial. If the investigator quotes the defendant about the deputy, there will likely be an objection on the grounds that this is hearsay, which will have the deputy statements stricken from the record and the Judge will instruct the jury to disregard the statement.).
Any-who, at some point the arrest is made and while we have the image of being put into the backseat, there are some occasions (usually misdemeanor traffic violations) where the officer will release you onto your own recognizance provided you make an appearance to do some paperwork in a timely manor (a couple business days, I got arrested in this fashion for a suspended license... long story short, DMV forgot to file paperwork saying I paid an earlier ticket, so the suspended license was an error on the states part.). Moral of the story, you can be arrested and not be taken "downtown" in the event of lesser crimes, though I'm not certain where this was.
Either, while under arrest she eventually is able to discuss the case with the cops and give her side. She tells them that there is evidence that ex-husband is lying and it's not her phone... evidence such as her paying the phone bill for that phone, a picture of her daughter texting with that phone, raise questions. For my story, I'm going to add that the husband is lying because the wife reveals he doesn't have visitation rights because this is likely not his first attempt at a hustle. This is much more searchable because the cops have access to the court records and can confirm this.
At this point, the evidence against the Ex-wife drops to the zero bar. Burden of Proof bar clears and Ex-Husband gets a new one and it rises all the way to lets say just under 99%. Basically, what's saving him now is that he's waiting for pre-trial motions to exclude any evidence which might give him wiggle room. After those motions end the prosecution evaluates the approach, and, providing there has been a significant barrier to conviction, will likely offer a deal to a lighter sentence in exchange for having to do a trial for this. Anyway, the only reason that Guilt of the crime and sentencing can only be assessed if the evidence points to a chain of events that could only happen in one specific way that anyone who does not believe "aliens did it" or some other similar non-sense would agree. Typically, this is why in Common Law Systems juries of random community members are asked to make the call. If 12 people with 12 different points of view can agree that the interpretation of the evidence presented (and nothing known from outside of the trial or the Judge told you to ignore during the course of the trial) is the only possible interpretation of the events in question and there are no different scenarios that can fit.
In the United States, the judge will give the jury a series of documents that will list all the crimes that the prosecution alleges. Typically, they are given the law or part of the law relevant to the case as is, and then frame it in a series of statemets that are rather binary. Typically they would look something like:
The Crime of CRIMENAMEHERE is determined to have occurred when the defendant has knowingly performed X action, while in the course of Y action, and Z event resulted. To convict Mr. Ex-Husband you must determine if
AND Mr. Ex performed X action.
AND Mr. Ex did so while in the course of Y action.
AND Z event occured because of these actions
AND Mr. Ex did so knowingly.
If you answer no to any one of these, you must find Mr. Ex NOT GUILTY.
If and Only IF you answered yes to all actions, than you must find Mr. Ex GUILTY.
(Each charge is written to this effect and each iteration of each charge is associated with one instance of the alleged behavior.).
If any thing can be answered as no, than it's acquittal and if any element could have an alternate explanation it's an acquittal, and if any evidence does not stay inline with the prosecution conclusion it is an acquittal. As was famously said in the OJ Simpson case, if the glove don't fit, you must acquit." That's pretty much what happened. Basically, some, but not all, of the evidence in that trial was called into question by the jury. Coupled with one of the first uses of DNA used in a case, which was quite difficult to grasp for any lay person that was living in a period of time that was 7 years before CSI better explained it to the average American... um... sort of... and the rather absimal way they were treated by both prosecution and defense lawyers who were trying to get ones who seemed unfavorable dismissed... and the mishandling of their sequestration... they really didn't want to stay together longer than need be... but the evidence issues were legit.