The prior here (A has stolen B's baby) is actually quite low. It just doesn't happen very often.

I know I'm nitpicking, but is the prior really that low in Solomon's case ? In our modern times, things like that almost never happen, but Solomon was living in Old Testament times (metaphorically speaking, seeing as the Solomon we're talking about here is just a character in a book). And the Old testament makes few legal distinctions between children and other kinds of property. Stealing them would still be a big deal, but hardly improbable.