Conditional Probability

In Probability,

In the real world, probabilities are not straightforward, like $P \rightarrow Q$. Therefore we translate into $P(B|A) \approx 1$. If $A$ happens, then B is most likely to happen. This defines as

$$P(B|A) = {P(A \cap B) \over P(A)}$$

This means

$${P(A \cap B)} = P(B|A) P(A)$$

$P(B|A)$ is the likelihood and $P(A)$ is the prior.