Information content of a random event

We define the information content information content of an event , once it occurs, as:

If an event is very probable (), then is a negative number with small magnitude.

If an event is very improbable (), then is a negative number with a large magnitude.

Negating gives us a number that is small when is probable and large when it is improbable. In other words, the less probable an event is, the more surprised we are when it happens.