'They contain the same content because A->B says that A and not-B is impossible, and saying that A and not-B is impossible says that A->B. For example, "it raining but not being wet outside is impossible."'

If you're talking about standard propositional logic here, without bringing in probabilistic stuff, then this is just wrong or at best very misleadingly put. All 'A->B' says is that it is not the case that A and not-B - nothing modal.