But suppose by careful investigation we had reduced it to two possibilities:

Just to be clear, this is obviously not what is happening with Eric. But let's run with the scenario:

Number 1 could theoretically happen by natural laws, number 2 could not. But number 2 is more probable anyway.

I would contest that this is not the case. If you think that n° 2 is more probable, I would say it's just measuring that the probability you assign to the supernatural is higher than 2^10k (besides, this is exactly Jaynes' suggested way to numerically estimate intuitive probabilities).
But your probability is just a prior: while n° 1 is justifiable by appealing to group invariance or symmetric ignorance, n° 2 just pops out of nowhere.
It certainly feels that n° 2 should be more probable, but the wrong answer also feels right in the Wason selection task.
This is what I was asking Eric: by what process were you able to eliminate every other possible explanation, so that the supernatural is the only remaining one?
I suspect also that, in your hypothetical scenario, this would be the same process hidden in the sentence "by careful investigation".