Information, confirmation, and conditionals

Given a measure I of information added, we can think of I(ac,b)−I(a,b) as a measure of the “deductive gap”, relative to b, between a and a∧c. When I(a,b)=−logP(a|b), I(ac,b)−I(a,b)=−logP(c|ab), the amount of information the indicative conditional 'if a then c' adds to b on Ernest Adams' account of that conditional. When I(a,b)=1−P(a|b), I(ac,b)−I(a,b)=I(a⊃c,b) where a⊃c is a material conditional. What, if anything, can be said in general about “information theoretic” conditionals obtained from measures of information-added in this way? We find that, granted a couple of provisos, all satisfy modus ponens and that the conditionals fall victim to Lewis-style triviality results if, and only if, I(a∧¬a,b)=∞ (as happens with −logP(.|b)).