Prior probabilities seem to me to be the key idea. Essentially, young earth creationists want P(evidence|hypothesis) = ~1. The problem is that to do this, you have to make P(hypothesis) very small. Essentially, they're overfitting the data. P(no god) and P(deceitful god) may have identical likelihood functions, but the second one is a conjunction of a lot of statements (god exists, god created the world, god created the world 4000 years ago, god wants people to believe he created the world 4000 years ago, god wants people to believe he created the world 4000 years ago despite evidence to the contrary, etc). All of these statements are an additional decrease in probability for the prior probability in the Bayesian update.