It would be interesting to see your estimates and probabilities.
It's good to keep in mind that much of evolution took place in simpler life forms with much shorter lifetimes than humans.
Example:
5*10^30 bacteria on Earth
Bacteria can multiply every 20 minutes.
2*10^15 minutes in life of Earth
up to 10^14 generations of bacteria
up to 10^44 bacteria lifeforms in life of Earth
Human DNA basepairs = 10^9.
So you need to evolve one basepair every 100,000 generations, with 10^30 specimens per generation. That doesn't seem totally impossible. And for reference 100,000 generations of bacteria is equal to about the age of the world since Christ, but we have observed bacteria mutating to adapt to their environments in lab experiments of observable duration.
And wait, there are 10^22 stars in the visible Universe so imagine you run the same experiment 10^20something times just in case you sometimes get vegetables instead of intelligent life. If it succeeded once, we are that success. If it's twice it's us and some other guys. Etc.
