If the MWI is true, then there must be some universes that would experience multiple highly improbable events. These events would be a hint to residents of that universe that the MWI is correct. Why wouldn't the usual Bayesian analysis apply here?
Imagine yourself as a resident of that "universe" (I prefer to think of it as "branch").
Why should a sequence of unlikely events be a distinguisher between different interpretations of a theory, which make the same probabilistic predictions as each other?