If a fact is known, you don't need the contribution of a random person.

If a fact is not known, how can some random person produce it? Out of what.

E.g. in the situation of a crime: only activities like crime scene investigation, and interviewing of witnesses can produce anything that can be called a fact.

Now so from all that have some collection of real facts from the investigation which do not add up to an absolute proof that some particular defendant "dun it".

The next best thing you could do is use some sort of probabilistic reasoning.

Well, what training in probabilistic reasoning do the these random people off the street have?

Probabilities should be quantified in concrete numbers. Instead of some flaky "shadow of a doubt" nonsense, there should be some 99.99% (or whatever standard level) confidence which is somehow calculated.