Proof by deduction is simple. For example:
All humans are mortal, and Bill is a human; Therefore, Bill is mortal.
However, proof by abduction differs. A famous example:
The lawn is wet. But if it rained last night, then it would be unsurprising that the lawn is wet. Therefore, by abductive reasoning, it rained last night.
There seems like a subtle difference, but it's actually huge as abduction is uncertain rather than certain.
Are there examples of mathematical problems that have been proven by only abduction, rather than by deduction or induction?
If there are examples of this, are they limited to problems related to probability?