When considering the "fine tuning" variation of the argument from design I think there's an important consideration that often leads people to error.
The various equations and formulas, and the constants that are used in those formulas, that we call "laws of nature" are just descriptions. They aren't causes. We observe and measure the universe, and we come up with these descriptions, and we express them as mathematical relationships that include constants such as the gravitational constant, or the speed of light, which is itself a consequence of two other constants, the magnetic and electric permeability of free space, and all those other constants that are found in our physics textbooks.
Because we have those numbers, we have a strong tendency to try and imagine what would happen if those numbers are different, but that is confusing cause and effect. The numbers are a description of the universe. If the universe were different, then we would need different equations that used different numbers. We can't just imagine tweaking the numbers and seeing what sort of universe there would be, because all of those numbers are as they are because the universe is as it is. If we have the atoms and particles and photons that we have, they are described by these numbers. If the numbers were different, then the universe wouldn't be described by them. Atoms wouldn't hold together. Matter and energy wouldn't interact as they do. The equations we use wouldn't be the same equations.
Because we use these numbers to describe the world, it is psychologically simple to imagine if the numbers were different, and we realize, in that case, that the universe simply wouldn't "work". At that point, we might begin to thank our lucky stars that those numbers are exactly what they are, and we might even be tempted to assign some sort of "probability" to those numbers being what they are, but such an exercise is meaningless. If the universe didn't work the way it did, the numbers and the equations that use them wouldn't be useful.
James Maxwell came up with a set of four equations that describe electromagnetism, and the elements in those four equations have elements that can be related to each other using two constants, for electric and magnetic permeability. What is the probability that those four equations would be useful to describe the universe? The question borders on the nonsensical. However, the "fine tuning" variation of the argument from design asks us what is the probability that those constants would be what they are. That question is equally nonsensical, but it doesn't "feel" quite as nonsensical.
We can't talk about probability in such cases. The question has no meaning. The equations and the constants therein are what they are because the universe is as it is. If the universe were different, there would be different equations, not just different constants.