There aren't an infinite number of possibilities.
First of all, a possibility ,loosely defined, is something or anything that can happen in a given situation. For this to be possible (able to happen) it means there are several alternatives through which events can take course, this alternatives are infinite only if we do not eliminate the illogical/impossible alternatives, which ,in the real sense, aren't alternatives since they cannot happen.
Something is only possible if there is a chance it can happen in a given situation,this means that a possibility is valid only if the chosen hypothetical alternative is logical i.e if the laws of nature (all forces of the nature both known and unknown), the laws of the land (in some cases) approve of it and the environment or surrounding make it possible (able to happen)
In some instances what we think is impossible might be possible, so what we think is an impossibility could indeed be a quite likely possibility. I think that what humans perceive as possibilities are also limited to our knowledge, imagination and ,as previously stated, the laws of nature and the laws of the land.
For instance, there's a bus in the Sahara Desert there's a large number of possibilities that could occur, maybe aliens space ship could hover above it and disintegrate it, capture it, race with it.... or the wheel/s could get a puncture.... the list is extremely long but not infinite, perhaps it is impossible to name all the possibilities, that however ,doesn't make the possibilities infinite but rather just too many to list/name . The suggestion that there's infinite possibilities would be like saying the bus will loose control and sink into an ocean in the Sahara... the environment doesn't allow for such an alternative, this is therefore an impossibility.
On the question of whether a blue dragon broke your dish i'd say with humanity's or rather, my limited understanding of reality that its indeed impossible , unless of course it was a tiny dragon, if any such creature does exist.