Well no, "probability 0" means "impossible". I'm not sure what difference you're seeing between "zero probability" and "zero chance", but they mean the same thing.
In mathematics, probability 0 means "almost impossible". Think about randomly choosing a number between [0,1]. Uh-oh, that set is actually infinite (cardinality aleph 1, technically). Suppose we consider only the numbers in it with 1 decimal digit, i.e. {0, 0.1, ... ,0.9,1}. Every one of them has 1/10 of probability of being chosen. Now, suppose we consider two decimal digits: 1/100 probability of being chosen.
Repeat this process and consider no discretization (i.e. there exists arbitrarily small epsilon>0 such that the difference between two numbers in the set is < epsilon).
Then the probability is.. 0! (you see how we divide 1 by the number of elements which are in the set)
But in the end you are going to pick one number or another in that set, so it is not "impossible". Surprise surprise.
