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?