 Continuing to restrict our attention to the case where the antecedent has non-zero probability, this argument-form preserves certainty: A\(\supset\)B; so A\(\Rightarrow\)B. The converse inference is uncontroversial. So if we were just concerned with certainty preservation, Hook and Supp would be equivalent. But they are far from equivalent for uncertain beliefs: the former can be arbitrarily close to 1 while the latter is 0.