From Probability and Random Processes by Geoffrey Grimmett and David Stirzaker-
An event $A$ is called null if $\Bbb{P}(A)=0$. Null events should not be confused with the impossible event $\emptyset$. Null events are happening all around us, even though they have zero probability; after all, what is the chance that a dart strikes any given point of the target at which it is thrown? That is, the impossible event is null, but null events need not be impossible.
Doesn't a probability of $0$ mean that the event cannot happen just like a probability of $1$ means that the event has to happen?