I consider myself towards the upper right. Sure there's a 0.0001% chance there is a god, but I care about significant digits. If something's existance has been reduced to mythological creature status like a phoenix, a cockatrice or a dragon, I can think with confidence that it's not worth the time entertaining the idea.
You DO understand a god doesn't necessarily mean something like an animal, right? A god can be anything, aliens, etc.
If it makes you feel better, ignore the examples I gave and I'll reword my statement.
Once something has become or is unlikely enough, I will dismiss it. Otherwise, you would have a mind so open that your brain will fall out. It doesn't matter if we're discussing gods, ghosts, zombies, spiritual energies, mythological creatures or even aliens, everyone has a certain breaking point or reality filter and this just happens to be one thing that doesn't get through mine. Just look at all the ridiculous things North Korea spurts out as another example. There's an incredibly small chance they were being honest about discovering a secret miracle drug which cures MERS, AIDS, Cancer and Ebola, but the existence of this drug is dismissed by just about everyone with free will because of how insanely unlikely it is. Frankly, I'd say it's more probable that dragons exist.