“Fine tuned” doesn’t mean “highly improbable” in mathematical or physical sense, because probability is defined only as a limit value in case the number of trials is infinite. Once you have only one outcome there is simply no "improbable" probability. Check your sources if they understand that much.

“Fine tuned” claimed by some people is currently only a metaphysical claim: “IF we believe that the physical constants can take any value, then only some exact constants define the Universe with the characteristics like ours.” Note if. There’s no real evidence for that belief, that all the values are/were actually possible. We don’t know if there’s something outside of the results of our current experiments that can support such claim, but given what we exactly know, there’s also no real reason to believe that the other constants were possible.

Note: we also have absolutely zero of exact evidence that multiverses exist. So what we actually have is only this Universe of ours, with only the constants that we observe.

To paraphrase one joke, if you only saw only one sheep, looking black, through you window in your whole life, moving from left to right, the only valid mathematical and physical claim you can make is "there exists at least one sheep there, whose one side is black." Nothing more unless you make more observations. It's basic scientific literacy.

Or to paraphrase another example: you've just went to your search machine and typed "seinfeld license plate picture." You've received the image of the plate on which is "new york assman." Then you go around saying "imagine, from all combinations that I can imagine that the license plates can have, I've got exactly this one. It's so improbable." No, it isn't. Sorry to burst your bubble. Now imagine a relaxed experiment: You live in New York, go outside your door, wait for the first car to pass by. You never saw any license plate in your life, or got any information how they are issued. Then you go out and see the license plate "BGY 3891." You say again "oh look, from all the license plates in New York, if I assume they can have 7 letters and digits, how 'improbable' it is for me to see exactly BGY 3891." Again, in that experiment, there's no mathematical probability involved. You simply observed one license plate. You can invent "fine tuning" story about it, of course: imagine, if the Earth wouldn't exist, there would be no humans, there would be no cars, there would be no license plates, there would be no me making the experiment. Yes. But given all that actually exists, and that you actually went and observed one plate, it's simply the first (the only) license plate you saw.

I've also generated a number of random bytes, hex encoded, which can be observed as one big number:

4ad41f5650977f991bb1b1a12a29f1cefe1e6ffede
8bb7d71ab0199832ca60345236ca343a0e3aff02fc
8b8a6d24aef012b3b15e688f3bcd7d82a77e3f0e35
6745b1a6d4bcd1fc90ff4e3ee273cb1f0989fa140a
b0a932252e9bf2ac3198b3bb7446a738d252233861
8ba380465181f544d900f8cc20b1544b6022f05bc5
266917d2ef5a8f6afe41245862b66c3c3f1874df84
c3bf6c4362455e2c4c66d08be68c1b1a0ab073619a
c5626e7719c4bc75d96ebb42daee9f147fe60aae71
85a482939c62ded6e05ac9728e7edf65c97c868535
63f697a45e75d325824e4bea051c1c3781fa284d86

And wow there are 10 to 556 (1 with 556 zeroes) possible numbers that big, and I've got exactly that one! Isn't it amazing? Hint: it isn't.