I have been asked to write an extremely short explanation of the Bayesian approach to evidentiary issues, for the benefit of those who regard themselves as probabilistically challenged. Although the application of Bayesian probability to evidence has generated a good deal of debate, its use as a heuristic device should not be particularly controversial. Evidence concerns propositions that are uncertain. Accordingly, some concept of probability must play a role. Standards of persuasion, such as "more likely than not" and "beyond a reasonable doubt" are clearly probabilistic, and the definition of relevant evidence, as expressed in Fed. R. Evid. 40 I, is explicitly probabilistic. The standard probability calculus expresses the probability of a proposition as a number ranging from 0 (for impossibility) to I (for certainty). The best interpretation of a probability statement, most Bayesians would say, is as a subjective assessment of one's level of confidence that the given proposition is true. Here's a simple example. Recently, I ran a 5K race with my 9-year-old daughter. She was aiming to come in under 30 minutes. Partway through the last mile, she asked me- this is the truth- "Can I break half an hour? Is there better than a 40% chance?" (Is there a genetically transmitted affinity for probability?) The question made sense, even though the race was a non-recurring event, and she was either going to break the 30-minute barrier or not. (She did, with 14 seconds to spare.)
Friedman, Richard D. "A Very Brief Primer on Bayesian Methods in Evidence." AALS Section on Evidence Newsl. (2002): 3.