A family of graphical hidden Markov models that generalizes hidden Markov chain (HMC) and tree (HMT) models is introduced. It is shown that global uncertainty on the state process can be decomposed as a sum of conditional entropies that arte interpreted as local contributions to global uncertainty. An efficient algorithm is derived to compute conditional entropy profiles in the case of HMC and HMT models. The relevance of these profiles and their complementary with other state restoration algorithms for interpretation and diagnosis of hidden states is highlighted. It is also shown that classical smoothing profiles (posterior marginal probabilities of the states at each time, given the observations) cannot be related to global state uncertainty in the general case.