I look at God as a human construct, not the reverse, i.e. humans are a God construct. Therefore for those who feel the need to construct God, he is every bit as real as a tree (p=1). For those with no need, he is non-existent (p=0).
Of course, there will always be those in transition or who can't decide, so that probability is somewhere in between. But it's generally a pretty clean cut.
The rub is not whether you believe or I don't, it comes when you or I decide to jam our belief down someone else's neck.
But to the original question, I see no way to objectively set a probability for the existence of God. The assumptions required to calculate such probability would never be widely accepted and therefore the answer would be meaningless to a significant piece of humanity.