If $A$ and $B$ are disjoint events, then $P(A\mid B)$ is?

Question

If $A$ and $B$ are two disjoint events, then would $P(A\mid B)$ equal 0 or would it just equal $P(A)$ considering $P(B)$ doesn't effect it?

Answer 1

$\mathbb{P}(A\mid B)=\dfrac{\mathbb{P}(A \cap B)}{\mathbb{P}(B)}=0$ because $\mathbb{P}(A \cap B)=\mathbb{P}(\varnothing)=0$.

Intuitively, because $A$ and $B$ do not occur together, given that we know $B$ has occurred, we know for sure that $A$ has not occurred. So the conditional probability of $A$ given $B$ should be $0$.

Answer 2

If they are disjoint, then $P(A|B)=\dfrac{P(A\cap B)}{P(B)}=0$, because $P(A\cap B)=0$.