A counter example: if we have two events $A, B$ such that $P(B)>0$ and $P(A)>0$, but $A \cap B=\emptyset$, then $P(A \mid B)=0,$ but $P(A)>P(A \mid B)$. It's easy to come up with examples like this: for example, take any sample space with event $A$ such that $P(A)>0,$ and $P\left(A^c>0\right)$, it follows that $P\left(A \mid A^c\right)=0,$ but $P(A)>0.$
