Consider P(E) = 1/3. We can consider three worlds, W1, W2 and W3, all with the same probability, with E being true in W3 only. Placing yourself in W3, you can evaluate the probability of H while updating P(E) = 1 (because you're placing yourself in the world where E is true with certainty.
In the same way, by placing yourself in W1 and W2, you evaluate H with P(E) = 0.
The thing is, you're "updating" on an hypothetical fact. You're not certain of being in W1, W2, or W3. So you're not actually updating, you're artificially considering a world where the probabilities are shifted to 0 or 1, and weighting the outcomes by the probabilities of that world happening.
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.
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?