I believe this would be correct if there were no examples of life already extant - but the fact that we exist shows that the probability of life and civilization arising is strictly greater than 0. Given an infinite universe with a flat probability distribution (i.e. there's nothing particularly special about our little corner), any >0 probability will occur an infinite number of times.
I highly doubt the actual universe is really infinite, however. Incomprehensibly big, yes.
I highly doubt the actual universe is really infinite, however. Incomprehensibly big, yes.