Ah, gotcha. I tried learning Bayesian probability once and failed utterly. One of the only classes I just barely passed (stat was the other). My brain just barely computes it.
The intuition is exactly your argument:
When the machine says yes it’s either because
(1) the sun went nova (vanishingly small chance) and machine rolled truth (prob 35/36) – the joint probability of this (the product) is near zero
OR
(2) sun didn’t go nova (prob of basically one) and machine rolled lie (prob 1/36) – joint prob near 1/36
Think of joint probability as the total likelihood. It is much more likely we are in scenario 2 because the total likelihood of that event (just under 1/36) is astronomically higher than the alternative (near zero)
I’m skipping stuff but hopefully my words make clear what they math doesn’t always
