Fine-tuning of the universe is not a cogent objection. It gets causality wrong. The idea of a set of knobs that God tunes to get it just right for life to be possible is wrong. The universe has not been tuned. Rather, matter and the four fundamental force of nature (gravity, electromagnetism, the weak nuclear force, and the strong nuclear force) exist, and we don't know how that came about. Matter interacts the way it does, and that happens to work the way we observe. Measuring G, h, c is just a description of those interactions, and just because we can replace those numbers with other numbers in theory, it doesn't follow that someone set those numbers deliberately. And if that explanation makes you feel unsatisfied or uncomfortable, then you either do something about it, or relegate the that too to the place where you keep all the things you also don't understand. There is no consequence, unless you make a pathetic stink about it.
Calculating the probability that number would be as they are only serves to reveal an absent understanding of how shaky ground the argument for fine-tuning pointing to God (as a general concept) is. The numbers exist on a uniform and otherwise unspecified range, and as such the probability of any set of particular numbers is zero.
"I'm trying to give you logos here, and you are asking for ethos. Why?! Is it because authority is more persuasive to you? Is that because you fear you won't understand the argument? Or is the topic just boring? Would you prefer pathos because that is the only kind of response you are capable of? Well here it is, my pathos. I weep for us, for our collective, as we are held back this way. We could be really somewhere..."
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