There are problems with talking to a zombie about qualia, and then extrapolating this kind of behaviour to other beings, especially one's self. In short, you can't actually believe what they say.
By asking a zombie about his qualia, it would, at least in the realm of gedanken experiments, be possible to to get a zombie to say that he does have an internal state, and that he strongly believes he does. But, since we know he doesn't, since he's a zombie, there is no question about the fact that he is incapable of actually believing he has an internal state, since beliefs are subjective. He can only act as if he had a belief – and that is all that has been happening with our zombie conversation.
It is therefore not possible for a person to believe he is not a zombie when in fact he is one, since a belief, although clearly behaviorally expressible, is subjective. A zombie cannot believe anything, so cannot believe he is conscious even though he isn't. We can therefore know that we are not zombies since we can believe that we're not zombies. Even believing we are zombies proves we're not zombies.
There is, of course the problem of solipsism with this issue. I know I am not a zombie, since I am able to ascertain I am not just behaving as such – as I can have a belief which is not behaviourally expressed – but I cannot know this about others. I only have their behaviour to go by. I may be surrounded by zombies and never know.