Actually, since there are infinite universes with infinite sun with infinite earths, the probability of life is Infinity / 10E164314 or rounded, 100%.
Probability of choosing a specific card is the same for any deck of cards...or life on any planet. Should we wish to stack the deck and use 52 decks to get a specific card...each individual probability is still 1:52. But to be fair and open to the possibility earth is the only lucky (or for democrats--unlucky) life place in the universe, the numbers are still daunting...and still probability zero for random life generation.
Current cosmologic models postulate that the universe is finite--about 109light years in radius. And remember most of it is empty space. Current estimates by cosmologists put the number of life supporting planets at about 1010. The magnitudes just aren't there given the complexity of assembling chemicals into life.
As for infinite universes...nice theory
And finally if you consider the entire known universe--increasing the number of primordial pools, assume all life would have not necessarily the same chemical structure, but the similar chemical processes, and give the entire age of the universe as available for genesis, the probability only reduces a few orders of magnitude. The probability life would develop at random still exceeds 10-100 000
Try it yourself. It's just simple statistical mechanics.