Even from one self-reproducing cell it would have been highly improbable that higher life should develop. And the probability that intelligent life, dominant through its brainpower (something I question sometimes), would develop, is even smaller.
Your conclusion is correct, of course. But still, why are you here? I mean, your consciousness, the thing that is you, is here, now. Why? You're not here anymore in two hundred years. It hasn't existed before. It's hard to believe that consciousness comes out of nothing.
Furthermore, it's not logical to say that the universe is infinite. Why? Because chances that a dominant species with faster-than-light-travel should have developed somewhere is not zero, thus it must exist. But I'm not a slave yet, so your argumentation leads me to the conclusion that the universe is not infinite.

So my argument remains valid.