§ Conditional probability is neither causal nor temporal

I found this insightful:

P(A|B) means the probability of A happening given B already
happened. Not so! P(A|B) doesn’t specify the time ordering of A and B. It
specifies the order in which YOU learn about them happening. So P(A|B) is the
probability of A given you know what happened with B.

This makes sense from the information theoretic perspective; I'd never meditated on this difference, though.
I'd seen things like:

P(sunrise | rooster-crow) = large even though rooster crowing does not cause
the sunrise to happen.

but I'd never seen/actively contemplated an example of P(A|B) where they are temporally reversed/ambiguous.