Rare things that have been documented much better than UFOs

[Mendel]

I would set the prior of visiting, physical interdimensional beings rather smaller than visiting, physical aliens, but surely much bigger than Leprechauns, those being supernatural.

No times 12, and no.
Interdimensional beings are exactly as fictional as leprechauns, and their powers are exactly magic.
There is no science of interdimensional beings because they contradict established science, and there's zero evidence for them.

What is the probability of something I imagined in my head to exist in reality?
It's zero, because I did not follow the evidence. There are no observations that point to them possibly existing.

They sound more science-y than leprechauns, but they really aren't.