quality:correction
As an axiom of probability

Some authors, such as de Finetti, prefer to introduce conditional probability as an axiom of probability:

This equation for a conditional probability, although mathematically equivalent, may be intuitively easier to understand. It can be interpreted as "the probability of B occurring multiplied by the probability of A occurring, provided that B has occurred, is equal to the probability of the A and B occurrences together, although not necessarily occurring at the same time". Additionally, this may be preferred philosophically; under major probability interpretations, such as the subjective theory, conditional probability is considered a primitive entity. Moreover, this "multiplication rule" can be practically useful in computing the probability of A ∩ B {\displaystyle A\cap B} and introduces a symmetry with the summation axiom for Poincaré Formula: