I don't have an answer to the question I think you're asking, but it's perhaps worth noting (if only to preempt confusion) that there are different notions of probability that may provide different answers here. Probability as a mental construct that captures ones ignorance about the actual value of something in the world (e.g., what we refer to when we say a fair coin, when flipped, has a 1/2 probability of coming up heads) has a smallest unit that derives from the capabilities of the mind in which that construct exists, but this has nothing to do with the question of quantum measure you're raising here.
Probability that a coin comes up heads is 0.5. Probability of N coins coming all up heads is 0.5^N. So what exactly was the original question in this context -- are we asking whether there exist a smallest value of 0.5^N?
Well, if the universe has a finite time, if there is a smallest time unit, if the universe has finite number of elementary particles... this would provide some limit on the number of total coin flips in the universe. Even for infinite universes we could perhaps find some limit by specifying that the coin flips must happen in the same light...
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.