The standard in civil trials is "on the balance of probabilities" or
"more likely than not." This is often expressed as "more than 50%
likely", but this question is meant to provide an edge case to this
standard of proof. Despite one person being provably innocent, could
all 3 people be found civilly liable for 1/3 of the damages, since
each individual has a 67% chance of having committed the crime?
General Rule: No
Generally speaking, the answer is "no". A plaintiff must prove liability by a preponderance of the evidence as to each individual defendant. This flows from the basic structure of tort lawsuits (a civil claim alleging damages suffered from criminal acts is a form of tort lawsuit).
The Narrow Market Share Liability Exception
There is pretty much only one circumstance where something similar to your example. But, it isn't strictly analogous because it only applies when all of the defendants can be proven to have harmed some of the plaintiffs and the only question outstanding is who harmed whom.
Defendants may be innocent of harming some of the plaintiffs, but can't be innocent of harming any of them, to face liability in this scenario.
This occurs which is when a class action lawsuit is brought against all (or almost all) of the multiple separate defendants who manufactured the products of the same type, all of which were defective.
A manufacturer of a defective product is strictly liable for all harm caused by the defective product, but usually a plaintiff must show precisely which defendant's product caused that particular person's injury.
But, in the class action context, where (almost) all of the people who made the defective products are sued by (almost) all of the people who were injured by defective products of that type, courts have allowed the class to recover an amount calculated to represent the aggregate economic value of the damages suffered by all members of the class combined.
Then, the aggregate damages award is allocated among the defendants in proportion to their market share of the defective product.
Then, the amounts paid to the class by the various defendants are then allocated to members of the class based upon the estimated damages suffered by each subgroup of class members (or in separate case by case damages hearings).
This is an exception to the usual requirement to prove causation against each individual defendant in the case of each individual plaintiff, because the risk of injustice by the process overall to any given defendant is small, and requiring proof of causation in this situation creates a burden on plaintiffs that lacks the justification that it would have if the injured parties had sued on a piecemeal basis.
But, this only works when the defect in the product was shared by everyone who made that kind of product, and was not simply a "quality control" issue in the manufacturing process.
For example, this kind of market share causation could be appropriate against all makers of tobacco products or asbestos or lead based paint. But, it would not be appropriate in a product liability case where some cars with built with substandard parts while others were built with parts that met the specifications for the cars and those that were did not cause any harm.