Here's a rough start of a theory of non-triviality of conditionals.
A material conditional "if p then q" is trivially true provided that (a) the only reason that it is true is that p is false or (b) the only reason that it is true is that q is true or (c) the only reasons that it is true are that p and q are true.
A subjunctive conditional "p □→ q" is trivially true provided that (a) the only reason that it is true is that p and q are both true or (b) the only reason that it is true is that p is impossible or (c) the only reason that it is true is that q is necessary or (d) the only reasons that it is true are that p is impossible and q is necessary.
For instance, "If it is now snowing in Anchorage, then it is now snowing in the Sahara" understood as a material conditional is trivially true, because the falsity of the antecedent (I just checked!) is the only reason for the conditional to be true. The contrapositive "If it not now snowing in the Sahara, then it is not now snowing in Anchorage" is trivially true, since it is true only because of the truth of the consequent. On the other hand, "If I am going to meet the Queen for dinner tonight, I will wear a suit" is non-trivially true. It is true not just because its antecedent is false--there is another explanation.
Likewise, "Were horses reptiles, then Fermat's Last Theorem would be false" and "Were Fermat's Last Theorem false, horses would be mammals" are "Were I writing this, it would not be snowing in Anchorage" are trivially true, in virtue of impossibility of antecedent, necessity of consequent and truth of antecedent and consequent, respectively. But "Were horses reptiles, either donkeys would be reptiles or there would no mules" is non-trivally true--there is another explanation of its truth besides the impossibility of antecedent, namely that reptiles can't breed with mammals and mules are the offspring of horses and donkeys.