an icepick through the keyhole

Your claim, as I understand it, is that it is not rational to accept a conclusion as probable on the basis of probable evidence.

Let's suppose this is true. Then invoking "faith" to support the conclusion is worthless. If it's rational to (repeating the example I gave before) starve to death because you don't have ironclad proof that you're food isn't tainted, then (by the standard you have offered) that's the rational course. Saying "it's rational to starve, but you must have faith and eat" is just double senselessness.

What you're offering is the straw man argument. You're upholding an untenable notion of reason, showing it can't work, and then offering faith as a rescue from failures of reason which exist only in your straw man.