My textbook, *Statistical Inference* by Casella and Berger, says the following:

Suppose that $A$ and $B$ are disjoint, so $P (A \cap B) = 0$. It follows that $P(A \mid B) = P(B \mid A) = 0$.

Intuitively, I don't see how this makes sense. We know that, if two events are disjoint, then the probability of them both occurring at the same time is $0$. And my understanding is that the converse is true; that is, if the probability of two events occurring is $0$, then the two events are disjoint. With all of that said, if the probability that both events $A$ and $B$ occur is equal to $0$ (that is, the events are independent), then I do not see how that necessarily implies that $P(A \mid B) = P(B \mid A) = 0$?

I would greatly appreciate it if people would please take the time to clarify this.