> We have no clue how likely it was at Earth that life developed at all. Maybe it was just a chain of many lucky coincidences that happen once in 10 billion years. How is distribution any relevant then?

Incidentally this is the "Rare Earth" hypothesis. There's a rather depressing book on this: https://www.amazon.co.uk/Rare-Earth-Complex-Uncommon-Univers...

The book Rare Earth covers this topic throughly. The conclusion they come to is that complex, multicellular life is likely extremely rare in the universe. But simple, microbial life may be much more common than we think.

http://www.amazon.com/Rare-Earth-Complex-Uncommon-Universe/d...

I once read a book called Rare Earth; http://www.amazon.com/Rare-Earth-Complex-Uncommon-Universe/d...

and the authors argued that the Earth has many unique circumstance necessary for the development of intelligent animal life that such life is probably exceedingly rare in the universe. The Earth/Moon and its stabilizing effect on the orbit, Jupiter the gas giant that protects the inner planets from asteroids and the development of an oxygen atmosphere, etc. and much more.

Perhaps "Rare Earth" by Peter Ward and Donald Brownlee.

http://www.amazon.com/Rare-Earth-Complex-Uncommon-Universe/d...

If you are really interested in this, read "Rare Earth", http://www.amazon.com/Rare-Earth-Complex-Uncommon-Universe/d..., it goes through an incredible mass of astronomical, geological, and biological information. It concludes that, because so many things had to go just right, and so many others were completely random, primitive life (bacterial-level) is likely to be more common than previously thought, while advanced life (multicellular) is likely to be much less common. Because of the sheer size of the galaxy, it is probable that other intelligences evolved elsewhere, but they are probably going to be too far away for any sort of contact, even receipt of potentially meaningful radio. It is a well-written book, despite the amount of information it is very readable.