If $A$ and $B$ are events such that $P(A \mid B)=P(B \mid A)$, then :

$A=B$ $A \cap B=\phi$ $A \subset B$ but $A \neq B$ $P(A)=P(B)$

$P(A)=P(B)$

$P(A | B) = P(B | A)$ $=\frac{P(A \cap B)}{P(B)}=\frac{P(A \cap B)}{P(A)}$, $P(A) \neq 0$, $P(B) \neq 0$ as  $P(X | Y) = \frac{X \cap Y}{P(Y)}$ so  $\frac{1}{P(B)}=\frac{1}{P(A)}$ $\Rightarrow P(A) = P(B)$