Some angles to consider:
1. We normally say high or low probability, and not big or small probability. We do say, however, that "X makes the probability of Y greater/smaller".
2. "Having this happened" is incorrect. It should be "...of this happening".
3. It is better to use "that" when you are talking about something remote. Something that is not likely to happen is something that is remote.
4. If you say, "There is a low probability of that happening", it means you think it is unlikely to happen. That sounds pseudo in daily life unless you genuinely have the probability statistics.
5. To me, it is much better English to say, "It is unlikely to happen" or "Chances are that it won't happen."
6. If you believe that "it may happen yet, however unlikely it seems" you could say just that, or you could say (if you are truly keen on using the word "probability"), "There is just a slight probability that it might happen." Even in this example, "possibility" is a much better word.
7. The second sentence is entirely incorrect because "potential" may not be used in this way and "of having this happened" is wrong.
8. My advice is to keep "probability" in your "less frequently used" compartment in your own style guide, unless you are writing your statistics or mathematics homework.