This paper deals with a different behavior of weak necessity modals (in Japanese, hazu) in comparison with plain necessity or possibility modals in their epistemic use. While the latter cannot be immediately followed by the negation of its prejacent, the former allows this. After reviewing some previous approaches to this fact in Kratzerian framework, we try to implement [14]’s insight in terms of an update semantics by [15], modified by [13]. We propose that hazu makes a (possibly) counterfactual update by revising CG with normalcy condition.