I was reading an answer by Bumble where the topic of modus tollens being valid but contraposition being not valid came up: https://philosophy.stackexchange.com/a/43004/29944
More importantly, there are logics in which contraposition is not valid at all. For example, in David Lewis' logic of counterfactual conditionals, A ◻→ B does not entail ¬B ◻→ ¬A. Also, in Ernest Adams' probability logic it may be highly probable that B given A, but not highly probable that ¬A given ¬B. So in general, when speaking of ordinary English conditionals, one cannot always expect contraposition to be safe. A noteworthy corollary is that in both the Lewis and Adams logics, while contraposition is not valid, modus tollens is valid. Some accounts of logic incorrectly run together contraposition with modus tollens and treat them as the same thing. While both are classically valid, they do not agree across all logics.
I don't doubt this, but I was trying to think of an English language example to illustrate this without success.
Hence the question: Is there an English language example, the simpler the better, where modus tollens is valid but contraposition is not valid?
An example where contraposition is valid but modus tollens is not valid would be nice as well, but I don't want this question to become too broad.