Infinate space

I have a question:

Modern science acknowledges that space is infinite. (I can't really get my head around the concept of something having no end but that's probably due to my tiny linear existence)

Some people think that life on earth is unique because the chances of it happening are so infinitesimally small.

If the universe is infinite, does that not mean that infinitesimally small sparks of life will crop up in infinite numbers of planets throughout an infinite universe.

Are we alone in the universe? I don't think so. I just think that alien life is so far away from us that we will never make contact.

Your thoughts?