You’re still implicitly saying that you’re 100% certain that it’s either a cat or a dog, which is wrong. If a horse picture has p(cat)=1e-5 and p(dog) = 1e-7, that should also be fine, right? And if you normalize those such that p(cat) + p(dog) = 1, you end up with basically p(cat)=1. Testing for (approximately) p(cat) = p(dog) when it can be neither is a messy way to go about doing calibration.

It’s just a long way of saying that having the probabilities not sum to one is fine.