Oh, and 'non-zero' is a probability term - it literally means 'not zero'. If there's any chance at all of a thing happening, there's a non-zero chance of it happening, whether that chance is 99% or 0.0000001%.
In this specific case I was basically using it to cover my ***. Didn't know whether he had or not, didn't have time to look, so: non-zero chance.