Here's a data point, do your own bayes accordingly:

I've frequently been able to solve mind or brain-related problems by doing actions conceptually similar to, or sometimes literally by, praying to God. I'm not a believer in any way, but the simple attempt to convince myself that I was communicating with some higher outside entity that had the power to solve my problem did solve my problem.

Here's the other evidence I have at my disposal, all of which I am confident above 90%:

1. My subconscious knows and understands everything - everything - that I think consciously, or even feel in passing.
2. My subconscious is much more powerful than my conscious with regards to such issues, with "power" corresponding here to having more input channels and more output channels for the same problem-solving ability.
3. My subconscious probably can figure out technical neurological or psychological solutions for things that aren't even in my (conscious) power to solve (either because I don't have the input to identify the properties of the problem, or to be aware of the exact nature of the problem, or don't have the output to affect the specific things in my brain / thoughts that need to be affected to undo the pattern causing the problem).

So by those assumptions, and a few other assumptions about base rates, it seems normal for me to conclude that my subconscious fixes problems for me when I "pray", as opposed to some deitic entity. But since you may not share my confidence in the above crucial beliefs, or my assumptions about base rates, the data point of my problems being solved by "prayer" might lead you to a different conclusion.