The correct version of this statement is "your belief over the beliefs that you will have after performing a test must be equivalent to your current belief", which seems to be a trivial claim.

It may seem trivial but then again so does the claim that P(A and B) <= P(A), and still...

In particular, I've sometimes caught myself simultaneously having aliefs like ‘if she flees, then she must be a witch’, ‘if she stays, then she must be a witch’, and ‘she may or may not be a witch, and I can't know until I see whether she flees or stays’, and until I read the post about conservation of expected evidence I never realized there was something wrong with that.