Formula of the probability of two dependent events
I'm wondering if there is a formula for the probability of two dependent events $A$ and $B$.
I know that if they are independent, the formula is:
$$ P(A \cap B) = P(A) \, P(B) $$
maybe if they are dependent there is an extra term?
The general rule for decomposition of joint events using conditional probability is:
$$\mathbb{P}(A \cap B) = \mathbb{P}(B|A) \mathbb{P}(A) = \mathbb{P}(A|B) \mathbb{P}(B).$$