It also requires knowledge of the laws that apply to determine which set of circumstances is more likely. And the determination of those laws requires observational evidence to establish them.<quoted text>
Arguing probability doesn't require "observable evidence". It simply concludes given a set of circumstances what is more likely.
To determine a probability, you need to know what the range of possibilities is and how many of those possibilities have the condition under discussion. Without *both* of those, it is impossible to determine a probability.
In the specific case under consideration, we are actually attempting to determine what is known as a conditional probability. Given the fact that the universe around us is as it is, what is the probability that there is a deity?
To determine a conditional probability, you need to know the range of possible universes which look like ours and then determine which of those has a deity and which do not. Clearly, we are nowhere close to even knowing what the range of possible universes is (is it even possible for the universe to be different---what does that even mean?). And we have no basis to determine which universes that look like our have or do not have deities that got them going.
So there is simply no way to even get started calculating a probability of there being a deity.
But, what we *do* know is that none of the scientific theories that agree with the evidence we have requires a deity to explain the universe around us. That alone suggests the probability of a deity is small.