So this "incredibly low probability"... am I to assume that while I sit by my fire, the vast majority of the heat is moving from a warm place to a cool place, but not quite all of it? I assume the heat moving from the cooler area to the warmer area is utterly overwhelmed by the heat moving in the opposite direction, rather like trying to piss up a waterfall.

What causes that "incredibly low probabiltiy"? Is it environmental, or completely random? Or do we not know?