I acknowledge that /u/you-get-an-upvote solved the question posed, I think there's another approach that's interesting.
I like the definition of Bayseianism that I saw in Aaron Brown's Red-Blooded Risk: A subjective probability is the amount that you would bet on an outcome (using a risk-neutral numeraire to get around technical issues with how people value money.) With that definition the answer is easy- a God's subjective probability might change with seemingly irrelevant information, but a mortal's would not. You must either pose a problem in the purely mathematical world where P|E is knowable, or the real world, where a probability is a subjective measure made by a human.