I am not sufficiently mathematical to be able to calculate the probability that the supernatural exists. However, I did find a paper by a Professor Nick Bostrom. He is (or at least was) a professor of philosophy and the Director of the Future of Humanity Institute at Oxford University. He was speculating about the possibility that we are living in a simulated reality and he arrived at some rather interesting conclusions.
You may recall that your original incredulity was inspired by the assumption that our technology is not up to it? Nick Bostrom's thinking went a little further. He supposed that some future civilisation might have appropriate technology to create simulations of their history - he called them Ancestor Simulations. The idea then is that we might be living in the ancestor simulation of some future civilisation. This means that what we might consider a technological limitation is seen by them as mere childs play.
He presents a philosophical argument for why they might want to do that, and some brief mathematical justification for the belief that they might have the ability to do that and arrives at a postulate:

Originally Posted by
Nick Bostrom
Posthuman civilizations would have enough computing power to run hugely many ancestor-simulations even while using only a tiny fraction of their resources for that purpose.
I found his definition of
Posthuman Civilisation a bit woolly. It was essentially,
they are civilisations that can do what I want them to do, in which case he could have chosen some other name, but, he didn't.
He then uses some rather basic probability maths to show that one of the following three possibilities must be true:
- The fraction of all human-level technological civilisations that survive to reach a posthuman stage is approximately equal to zero.
- The fraction of posthuman civilisations that are interested in running ancestor-simulations (or that contain at least some individuals who are interested in that and have sufficient resources to run a significant number of such simulations) is approximately equal to zero.
- The fraction of all observers with human-type experiences that live in simulations is approximately equal to 1
If the first of these is true, that means that humanity will not reach posthuman civilisation status and therefore we are not living in a simulation because there is no one to create it.
If the second is true, virtually no posthuman civilizations decide to use their resources to run large numbers of ancestor-simulations, in which case we are almost certainly not in a simulation.
If the third alternative is true we have two intriguing consequences.
- If we are living in a simulation, then the cosmos that we are observing is just a tiny piece of the totality of physical existence. The physics in the universe where the computer that is running the simulation is situated may or may not resemble the physics of the world that we observe. While the world we see is in some sense “real”, it is not located at the fundamental level of reality.
- If you believe that future civilisations will be capable of and interested in running ancestor simulations, then you must also believe that we are living in one!
One interesting consequence of this is clearly that the posthumans running the simulation would be equivalent to Gods in the eyes of the humans in the simulation, so, if you believe that future civilisations will be capable of and interested in running ancestor simulations you also have an explantion for God.
Clearly this whole idea did not meet with universal acclamation and he has not been feted as the new messiah or swept the board of all the philosophy prizes for his paper. There were newspaper articles (both for and against) and some more scholarly articles and papers quibbling about bits of it. Then Professor Bostrom rebutted the rebuttals and so on. I found a website that collected some very readable materials together,
which you can find here.
I'm still working my way through them, and whilst I am not convinced I believe in the possibility it is interesting stuff, nonetheless.