"If P(Y|X) ≈ 1, then P(X∧Y) ≈ P(X). Which is to say, believing extra details doesn't cost you extra probability when they are logical implications of general beliefs you already have."

Shivers went down my spine when I read that; this is the first time that I actually looked at a formula and really saw what it meant. Ah, maths. Thank you, Yu-el.