I would say less than 1%. That is if you were to bet me $1 that next year someone will mathematically prove that, I would bet up to $100 that it doesn't.
I am not talking about statistics here but uncertainty. Probability in the Bayesian sense is just a measure of how certain you are of something.
I can't prove that the sun won't rise tomorrow. Even if we didn't have any scientific understanding of what the sun was or why it appeared to orbit the Earth, I still would bet at great odds that it would also rise the next day.
So what is the certainty that the universe was created by a conscious creator? Well we can look at all the possible explanations and assume they have equal probability. Then you can use Occam's Razor and assume that simpler hypotheses are far more likely to be true than more complex ones (and a god is a rather complex one as it has to explain the existence of an intelligent being with the power and desire to create universes.)
You can call this a "philosophical" argument or a "scientific" one, or something else entirely. Science is basically the same thing, assuming simpler theories over more complex ones, and assigning certainty to different theories.
Also there is nothing special about religion. All the same arguments would apply when talking about, say, the existence of an invisible pink dragon that resides in my garage. I'm guessing your certainty of that is rather low though.