You can not ever discover in a statistical test that some probability is 0 or 1. Those are impossible values.
You can get arbitrarily close to them, but you can never reach those values.
Of course, they are valid values for the set of probabilities, just like 0K is a valid temperature, and c is a valid speed for massive things. You just will never see any of those.
No, the issue you’re referring to applies to anything estimated directly from a sample; there’s nothing magic about zero or one. If you see 5000/10000 heads, the maximum likelihood estimate for that proportion is 0.5, but it still has some uncertainty attached: the 95% CI is about [0.49, 0.51]. With more data, you can shrink that interval, but you can never collapse it completely. On the other hand, that same data does let you assign exactly zero probability to the hypotheses “the coin is all heads” and “both sides of the coin are tails”, since you’ve seen counterexamples of both.
> You can not ever discover in a statistical test that some probability is 0 or 1
Sure you can: if you are using inferential statistics and trying to determine the population incidence of some trait and every sample has a sample incidence of exactly 1 then the population estimate will be exactly 1. And that works the same way for 0, or any other value, too.
> c is a valid speed for massive things.
No, it's not. An object with any rest mass would require infinite energy to reach c. It's an excluded upper bound, not a valid speed.
Of course, they are valid values for the set of probabilities, just like 0K is a valid temperature, and c is a valid speed for massive things. You just will never see any of those.