I think this article may help.
I take it that P(Z) is your unconditional probability density and p(Z|x) is your likelihood function. Then taking the joint density p(x)p(Z|x) you can use Bayes Theorem for the posterior density which is the conditional p(x|Z)=p(Z|x)p(x)/p(Z).
I'm not sure why you think the unconditional and conditional probability densities would be equal unless, of course, the prior density and the posterior density were equal. It appears that the MMSE estimate applies to the posterior density p(x|Z).
EDIT: The link is a bit slow, but works as of my testing at the edit time.