Logic doesn't work when you're incorrectly using facts. Light has velocity. We can only see the stars that are as close to us in light years as the universe is old. Not to mention light gets weaker as it goes farther. In the middle of the night, shine a flashlight on your house. Now start walking backwards. Keep walking backwards. The circle of light will get bigger andOk, number one, the universe is not infinite. The reason we know this is because if the universe was infinite, then there would be an infinite number of stars in it, and every star would put out light....so if the universe was infinite, and you looked up at the night sky, then the night sky would be blazing with light, because there would be a beam of light coming from every direction.

The chances are slim, true. Let's say that the chances of life evolving are one in a million. But there are trillions of planets in the galaxy. SO even if the chances of life evolving are tiny, there are still thousands of alien civilization out there. (See the Drake equation)
Three things:
- The Drake equation doesn't help us at all, because we don't know any of the variables in it.
- The Drake equation doesn't help us at all because it is for calculating the chances of humanity encountering alien lifeforms, not the chances of them being there.
- I believe that you mean there are trillions of planets in the universe. The milky way is estimated at 200 billion stars.