When you update, you're not simply imagining what you would believe in a world where E was true, you're changing your actual beliefs about this world. The point of updates is to change your behavior in response to evidence. I'm not going to change my behavior in this world simply because I'm imagining what I would believe in a hypothetical world where E is definitely true. I'm going to change my behavior because observation has led me to change the credence I attach to E being true in this world.
There's a labeling problem here. E is an event. The extra information you're updating on, the evidence, the thing that you are certain of, is not "E is true". It's "E has probability p". You can't actually update until you know the probability of E.
What the joint probability give you is by how much you have to update your credence in H, given E. Without P(E), you can't actually update.
P(H|E) tells you "OK, if E is certain, my new probability for H is P(H|E)". P(H|~E) tells you "OK, if E is impossible, my new probability f...
It seems like in order to go from P(H) to P(H|E) you have to become certain that E. Am I wrong about that?
Say you have the following joint distribution:
P(H&E) = a
P(~H&E) = b
P(H&~E) = c
P(~H&~E) = d
Where a,b,c, and d, are each larger than 0.
So P(H|E) = a/(a+b). It seems like what we're doing is going from assigning ~E some positive probability to assigning it a 0 probability. Is there another way to think about it? Is there something special about evidential statements that justifies changing their probabilities without having updated on something else?