§ 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.