I've been saying for a while that I think fine tuning arguments are bad arguments. I want to explain that.
Suppose I shuffle a deck of cards and let you draw one. It is the queen of hearts. What was the probability that you would draw that card? Think carefully before answering!
Did you answer "one in 52"? If so, you're wrong. It was a pinochle deck, so your chance was one in 24, not one in 52.
OK, now I shuffle a different deck and you draw one. What's the probability that you draw the queen of hearts now?
If you responded, "I don't know, you didn't tell me what deck you are using," you are correct! In fact, this deck was a magician's deck in which every card is the queen of hearts. So then probability was 100%.
One more: I hand you a card with a bunch of unknown symbols on it. What was the probability that you got that exact card?
I'm sure it's clear where I'm headed with this. The only possible answer that makes any sense is "I don't know." The probability is, as the philosophers say, inscrutable.
You could, of course, make up some probability calculation. Say I pixillate the card by covering it with an n by m grid. Then I count how many pixels have black ink. Say I find M pixels. Next, I work out the number of ways that M things can be chosen from N = n*m things. Mathematicians call this number "N choose M." Finally, I declare that the probability that I got this particular card is one in N choose M.
That calculation would make sense if I knew that this card was produced by a machine that randomly put spots of ink in a grid on the card. But I don't have any reason to think this card was produced by such a machine. In fact, I have good reason to think it wasn't produced by such a machine, because if it was it is highly unlikely that the result would look like recognizable symbols.
There are several mistakes here that fine tuning arguments make. First of all, a probability calculation only makes sense if you have some idea of the probability space - the space of possibilities from which the output is drawn. The probability space is the "deck." If I have no idea what deck is being used, then I have no idea what the probability is for any given outcome.
We don't have a lot of universes to take data from - we only have one. So we don't have any idea of what the "deck" is: what sort of variation is possible for the supposedly fine tuned parameters.
Secondly, a probability calculation only makes sense if you have reason to believe that a probabilistic process is occurring. In the case of symbols on a card, we don't have any reason to think that the ink was deposited according to a random process. Likewise, in the case of the parameters that set our scientific description of the universe, we have no reason to think that they were determined by a random process. (In some string theory-based models, the parameters are reshuffled randomly when a baby universe is born. But in these models, there is an infinity of such baby universes, so the model provides the solution already. In any case, these models are highly speculative.)
Folks arguing via fine tuning begin by making up a probability space: for instance, Collins's "epistemically illuminated range." Then they pixillate that range in an arbitrary way, usually by assuming a uniform distribution of probability over the range. This leads them to some value for the probability of that particular parameter - but that probability is completely arbitrary, just as much as the probability we calculated for the card with strange symbols on it.
Bottom line: unless you have reason to believe that the "fine tuned" parameter was chosen by a random process from some given range, any calculation of probability for the value of that parameter is meaningless and arbitrary.