A single zero probability event suffices for the honest man. The claim that there are an infinite number is a didactic device with one purpose -- to deceive. This permits the proselytizer to retort that even though every single zero probability event he is capable of itemizing is shown instead to have a probability of one there are still an infinite (not itemized) number left to substantiate his false claim.
A famous biologist (I forget who) once replied "Statistics are for losers" to a colleague who requested numerical data supporting the biologist's thesis. By this he meant that understanding how something actually works cannot be achieved by simply measuring a few parameters of the system and calculating averages and variances. Once the mechanism is described and the processes determined it is possible to predict the behavior or response of the system without resorting to statistics.
It is also well known that statistics can be manufactured to suit any purpose (e.g., "How to Lie with Statistics"). Nowhere is this fault more apparent than in the purposely deceitful use of statistics to "prove" that known events (i.e., evolution) did not happen.
A single zero probability event suffices for the honest man.
I take it you do not believe in evolution. Or are you claiming to be dishonest?