“P(XXXYYY|H0) = 1 / 6choose3 = 5%. Wow, that's not a very good update for H0. It's probably just false. For expediency, let's just toss it out.” It only makes

“P(XXXYYY|H0) = 1 / 6choose3 = 5%. Wow, that's not a very good update for H0. It's probably just false. For expediency, let's just toss it out.” It only makes sense to toss H0 out if P(XXXYYY|H1) >> 5% (such that the evidence for H1 relative to H0 increases after the observation). You are implicitly assuming that’s the case because “it makes sense”. But as the parent post mentioned, the likelihood is not defined and in particular if the noise in the observation process is large enough, P(XXXYYY|H1) may be very close to 0.05 as well.