Treating it as one in fourteen million is, I suspect, perceptually impossible for humans without training. I suspect that without practice people don't have a feel for less than ten percent. (I sure don't and I've actually tried to, therefore everyone else has the same problem ... but they do in fact seem to.) But people observably just don't shut up and calculate even as they concede the lottery is way below their perceptual level.

I wonder if work's been done to measure just how good humans are at feeling probability, with or without practice.