I know next to nothing about these probability calculations but apparently physicists consider various possible scenarios that a universe could be, subject to fundamental physics theories such as quantum mechanics and general relativity, and then they can calculate the probability of a certain type of scenario. The type of scenario that allows existence of life then seems to have a low probability. But if we assume that all possible scenarios are realized in different universes or in different domains of our own universe, then we necessarily live in that type of scenario where life is possible, even if the number of scenarios of that type is a very small fraction of all possible scenarios and thus that type of scenario is very unlikely. This is how Steven Weinberg relatively successfully predicted the value of the cosmological constant back in 1980s.

The idea that there are other (unobservable) universes raises doubts but I think it's a pretty natural metaphysical idea. Why should some possibilities exist and others not? Existence and possibility may actually be the same.

We really have no idea if things like constants could even be other than they are, we really have no idea if the world would or wouldn't work anything like it does if things like constants were other than they are, and there's absolutely no way to estimate the probability of any of this stuff.

The problem lies in elevating mathematical equations to ontological status. They are not. They are merely symbolic representations that are useful as tools.

It would be more appropriate to say that if the universe was different then physics would be different, which it would be. However, the universe is what it is and we continue to create new mathematical symbolism as useful tools for describing and living in it.

To determine the probability of something, you have to establish a baseline to compare it to. Seeing as though we only have one universe to talk about, and nothing to compare it to, we can't sensibly come to any conclusions about probability, excepting that there is a 100% chance that universe under the exact conditions of ours will turn out exactly like ours.

Just Six Numbers; The Deep Forces that Shape the Universe, Martin Rees, is about six numbers that describe aspects of the universe that, if they were different, we wouldn't be here.

Rees sidesteps issues with Anthropic theories by casting his lot with multi-verse theories. His idea is simply that it makes more sense for there to be - have been - many "universes" along with ours coming and going as kinds of bubbles in a boiling ultra-verse stew, most of which don't work. That is, that ours is one of very many, and not merely a one-shot wonder.

In no way does this resolve ultimate mysteries - rather it makes them more remote - but it does account for the seeming utter unlikelihood of our universe being the way it is when it could have been so many other ways.

For me it doesn't make any sense to talk about probability in this way because there is a confusion factor that lies in the very existence of probability which exist only because of our own existence. Nor does it make sense to speak of probability for events that already occurred and for which the notion of probability no longer applies : for me there was a 100% chance that our world exists because precisely, it exists.

I have also another theory. In fact, in quantum mechanics each state of matter is defined by a certain probability as long as the observation has not been made. Once the observation is made, the probability collapse and reality takes shape and cannot be changed. But for me, this works also for our universe and considering that the only one where observation is possible is ours, there can be no other universe than ours. Finally, this is just another way of expressing my first paragraph..