Conditional probability is the probability of an event *given another event*. Think of this as the overlap in the Venn diagram, where the sample space is reduced to the area of $B$. We can calculate the probability of $A$ given $B$ as the intersection of the Venn diagram (i.e., the intersection of $A$ and $B$) divided by the probability of $B$.
$P(A | B) = \frac{P(A \cap B)}{P(B)}$