Two standards that I've heard of are "compelling" evidence, and "reasonable indication." Apparently, they may be used to defend certain actions where the level of proof is less than 50-50 but "non-trivial." How, for example, can evidence be "compelling" while being "less likely than not?"
The standard of proof required to survive a motion to dismiss is very low.
The factual (not legal) assertions of the plaintiff are assumed to be true, and the case is dismissed if the defense shows that even when the plaintiff is given that benefit, the assumed facts don't establish the case.
This standard is somtimes referred to as "sufficiency of the claims".
"Probable cause" is a disturbingly subjective and vague standard that is nevertheless central to the criminal justice system: "Probable cause" is the standard that justifies everything from search to arrest to a judge's decision in a preliminary hearing to hold a person for trial.
Black's Law Dictionary explains:
Facts and evidences that lead many to believe that the accused actually committed the crime. A probable cause is not a fail proof evidence as it only provides enough grounds to deem the convicted guilty of the crime, and thus to arrest and put the accused to trial.
(US only. A lawyer but not your lawyer. Information only, not advice)
"Mere scintilla." possibly "Reasonable belief," depending on circumstances and finder of fact.
If you search for "Proof chart", you'll find a lot of stuff about alcohol proof, but more importantly, diagrams that purport to show the relationships between different standards.