The notation is convenient sometimes, but other times it obscures whatâ€™s going on, like in the definition of conditional independence and the law of total probability (when you fix the conditioning event).

We can rewrite as to make clear that we are
deriving a *new* probability measure () *induced* from the old
one () using the knowledge that occurred. Or we could shorten
it even further, from to .

## Conditional Independence

Conditional independence reduces to regular independence under the measure . becomes .

## Total probability

, which is easier to see if we write it as .