We Are Probably Alone

We've all done it. On a clear night, probably far from the lights of the city, looked up at the dizzying amount of stars and wondered, "There's no way we're alone." The universe is too large for there not to be another planet inhabited with intelligent life.
But this thinking is a little off to me.
The universe is not infinite, it's damn big, but it has limits. This means possibilities are not infinite. Almost anything can exist but everything can't.
Also, the universe exists in time as much as it does space. Our existence does not amount to a blip on the universe's timeline. If another Earth does exist, what are the chances that it does during our time as a species.
And what do we actually consider to be life. Bacteria? Perhaps we can't even comprehend what another living planet looks like. Our own humanity colors our perception.
I'm not saying I don't believe in extra terrestrial life, it's a definite possibility, even probable. But it's not definite.