You need to be a lot more precise. It is a chore to figure out what you're talking about in some of these comments and we've gone several rounds and I'm still not sure what your thesis is.

once we make that assumption of knowledge in our own world, "would" applies to the set of logically possible worlds, which may or may not have a "bridging law" to produce qualia. Chalmers doesn't seem to address the probability of them having such a law given the physical causes or ontology that we find in A.

I think what you're saying here is that qualia will be found in the entire set of logically possible worlds physically identical to our world (any bridging law is non-physical we'll stipulate). Some of these worlds might have some kind of 'redundant' bridging law- but even if that isn't nonsensical we can ignore it.

Now, we can recognize that someone could discover that 2+2=3 but that doesn't mean 2+2=3 is a logical possibility in the sense that there exists a logically possible world in which 2+2=3. Rather, we would just conclude that the world we live in isn't logically possible under whatever system of logic is shown to be contradictory. If you want to do calculations that don't assume classical logic and the system of real numbers then you need do them over a larger set of worlds than those that are merely logically possible (what business you have doing calculations at all if those worlds are 'live' possibilities, I'll leave to you).

Now I agree with you that if we can be certain about the internal observation that leads us to conclude we have qualia then it follows that a bridging law is unnecessary as p-zombies also believe they have qualia for the same reasons non-p-zombies do. For p-zombies to be possible then, requires that mechanism to be unreliable. I'd be surprised if Chalmers actually argues we can be 100% certain we are not p-zombies-but alright lets say he does argue that. We can easily strengthen the argument as you suggest by simply saying that the cognitive mechanism that produces the belief that we possess qualia is not 100% reliable.

And in fact the worlds in which this cognitive mechanism fails are the worlds which, according to Chalmers, have no bridging law. As far as I'm concerned that solves the problem. We've answered the question which is- are there logically possible worlds physically identical to this one where Chalmers has no qualia. The answer is yes- those worlds in which the cognitive mechanism which alerts him of his qualia fails.

Whether or not those worlds are common, that is whether or not it is probable we are in such a world, is totally tangential to Chalmers argument. I don't see the point of your equations and what they mean doesn't make much sense to me- you seem to be conditionalizing on an argument and not evidence at times, which is confusing and controversial.