You've the advantage of me there, then, since in the context of gods I can't even see how the concept of possibility applies, personally. Possibility has to be grounded in something concrete - something, however minuscule, that we already know - to make any sense.
For example, I can have a pretty well informed conversation about the possibility of life on other planets because both terms in the discussion - life and other planets - have some substance. I know what it would mean to discover life on a different planet based on my pre-existing knowledge of and familiarity with life on this one. This is completely unlike the situation with gods - I've never encountered one and have absolutely no knowledge of any (not least because those who purport to believe in such things are notoriously poor at defining them concretely), so that when I'm asked if I'm open to the possibility of gods the standard response from me is that the concept of possibility doesn't even apply. What is it that I'm supposed to think possible, exactly?
Yes, this pretty much sums up my position as well. If the definitions we get given of god are either in my view logically contradictory or meaningless then the concept of possibility cannot be appllied any more than the possibility of jupremangandi existing.
A god if it exists doesn't necessarily need to accord with the (pretty clearly manmade) imaginings we currently see from theists. So I remain of the mind that the possibility still remains. But I'm not going to spend my life worrying about this. While there is no evidence I'll continue not to believe in the existence of god or gods. If something happens that provides that evidence in my lifetime, then so be it, I'll deal with that then. But I'm not going to start changing my life or my beliefs in the meantime.
Thinking about it a little more, perhaps my view is due to the fact that I am a scientist.
As a scientist I use evidence to derive theories, which provide the best model to explain the evidence. But I am always open to the possibility that the current theory could be disproved by the appearance of new evidence in the future. While it might be very unlikely for the most well evidenced theories that possibility remains and as a scientist you must always be open to that possibility.
So currently there is no evidence to support a view that god or gods exists. Therefore that view or belief is rejected. But however unlikely, you shouldn't discount the possibility of being wrong and that new evidence might arise that turns you view on its head. But note that this requires evidence.