Surprisal

In Information Theory this is called the suprisal and is calculated for a single outcome.

$s(x)=\mathrm{lo}{\mathrm{g}}_2\left(\frac{1}{p(x)}\right)=-\mathrm{lo}{\mathrm{g}}_2(p(x))$

If a probability is equal to $0$ then the surprisal is infinite and it is zero when the probability is $1$.

The Expectation of multiple possible outcomes of surprisal is called Entropy.