Right now I'm leaning against. It is a bigger job than I want to attempt for my posting debut. Sorry. Maybe someday.

But the basic idea was mentioned in this comment and there are links to some follow-up material in some of the comments. It is not that big a deal, but it seems to me that everything becomes a little more intuitive when you are adding and subtracting "surprisals" rather than multiplying and dividing probabilities.