As a partial answer, note that you will get extremely different results for P(H|E) depending on your choice of hypothesis H and evidence E. In particular, while naively E here is “Ms X won the lottery 4 times”, I think you’d still be posting the same question if instead you’d heard that “Mr Y won the lottery 4 times”, or more importantly, any other extremely unlikely positive-valence event (“Ms Z was struck by a bullet in the tiny area that happened to be protected by an object in her pocket”, etc). Which means that your E should perhaps be “some lucky unlikely thing happened to someone at some point in history”, which no longer seems very low probability after all.
Also the jump from “there’s something weird here” to “the Christian god did it” is too big—even if we do decide that some extraordinary explanation is required, our hypothesis space should at the very least include other gods :) and perhaps more realistically, things like bugs in the lottery program, collusion with corrupt lottery officials, etc.
As a partial answer, note that you will get extremely different results for P(H|E) depending on your choice of hypothesis H and evidence E. In particular, while naively E here is “Ms X won the lottery 4 times”, I think you’d still be posting the same question if instead you’d heard that “Mr Y won the lottery 4 times”, or more importantly, any other extremely unlikely positive-valence event (“Ms Z was struck by a bullet in the tiny area that happened to be protected by an object in her pocket”, etc). Which means that your E should perhaps be “some lucky unlikely thing happened to someone at some point in history”, which no longer seems very low probability after all.
Also the jump from “there’s something weird here” to “the Christian god did it” is too big—even if we do decide that some extraordinary explanation is required, our hypothesis space should at the very least include other gods :) and perhaps more realistically, things like bugs in the lottery program, collusion with corrupt lottery officials, etc.