EN, there are two main approaches to or interpretations of probability: the frequentist and Bayesian approaches. See https://en.m.wikipedia.org/wiki/Probability_interpretations
The frequentists won’t be able to do much with your God example. A Bayesian might be able to.
A Bayesian starts with priors (a model) and then based on observations calculates conditional likelihoods and updates those priors. Eg given some prior on the distribution of possible universes with or without the supernatural of some form (which includes a model of the probability in each such universe of whether sentient beings would be able to observe the supernatural), then given we are sentient beings in a universe and can’t observe the supernatural, one could calculate the likelihood that the supernatural exists in our universe.
Bayesian approaches have been very successful in science and econometrics, and are big in AI.
The problem with your example is of course it all rests on your priors as you can’t make many observations. But still, if you take unbiased priors together with a plausible multi-universe framework, you may get some sense of how unlikely it is that a supernatural force exists even though we can’t observe it. 1 in 3, 1 in 100?