General multiplication rule

The rule is $P(A \cap B) = P(A) \cdot P(B \mid A)$, where $\cap$ is the intersection symbol (A and B) and $P(B \mid A)$ is read the probability of B given A. No independence is required, because the conditional factor already accounts for any way the first event shifts the second. Drawing two cards from a standard 52-card deck without replacement, $P(\text{two aces}) = \frac{4}{52} \cdot \frac{3}{51} = \frac{1}{221} \approx 0.0045$. When the events happen to be independent, $P(B \mid A) = P(B)$ and the rule collapses to the simple product.