# Why conditional probability is conceptually difficult, even for Erdös

The short answer The expression, $p(a|b)$, read as the probability of “$a$ given $b$”, or as the conditional probability of event $a$ with respect to event $b$, cannot generally provide the probability of “$a$ given $b$” using the same probability function that assigns probabilities to $a$ and $b$. This is because such an event does not exist in the same space as $a$ and $b$. In fact, $p(a|b)$ is just a notation expressing the ratio of two probabilities.