Probability is a b*tch when you have infinity to hit the odds.
But you don't have infinity. You have, probably between 10 and 20 billion years for the universe, a few billion years for the earth, and a much smaller period of time for the higher life forms.
The available space and time is far smaller than the astronomical string of coincidences.
Umm, the universe is not infinite, is it is finite, and the we are not talking about eternity, but a finite amount of time. Given these two constraints, the odds are against the complexity of all life arising out of random processes.