Ahhh, that helps clear things up. For some reason I’d been understanding you as saying that, given P(Guilt|A) = 1, P(A|Guilt) was also 1. It looks like what you meant was just that Guilt is evidence for, but not necessarily 100% proof of, A. Am I getting that all correct?
Ahhh, that helps clear things up. For some reason I’d been understanding you as saying that, given P(Guilt|A) = 1, P(A|Guilt) was also 1. It looks like what you meant was just that Guilt is evidence for, but not necessarily 100% proof of, A. Am I getting that all correct?
Yes.
P(Guilt|A) = P(A|Guilt) only when P(A) = P(Guilt). In which case it would be 100% proof. But that is a rare situation.
Nitpick: the two conditionals also be equal if A and Guilt were mutually exclusive. (in that case, of course, the two conditionals would be both zero)