Given that we only know of one planet that contains life, you can't possibly draw the conclusion (that aliens are statistically likely to exist). You're assuming the only requirement is that a planet be in a star's habitable zone - but you have nothing to base that assumption on.
You can't extrapolate a line from one point.
From what we know, liquid water is required to sustain life. For observational purposes we have a sample size of (1) planet which resides in the habitable zone for life to exist, and that one planet contains life. The sample size is small, but it is at least as good a bet that life exists on one of the millions of other planets in the same situation as ours that exist in our galaxy as it is to bet against it.
The oldest undisputed evidence for bacterial life on Earth is 3 billion years ago, but other evidence points to life existing 3.5 or 3.8 billion years ago, not long after the Earth cooled enough for liquid water to exist on the surface. We've found water on Mars, the moon, in the atmosphere of Venus and on other moons in our solar system as well as in comets that visit the inner solar system from the Oort cloud. Since water is made up of two of the three most abundant elements in the universe that is hardly surprising. I think it would be a very safe bet that some of the 80+ million Earth-sized planets in the right orbits for water to exist as a liquid would have it on their surface.
As far as life coming into being, we don't know. But again, we have a sample size of 1 and 1 positive result. We have 80 million candidates to choose from in our galaxy and 100 billion other galaxies to look at. To assume that life wouldn't exist anywhere else would be a much less tenable position than the reverse.
What we need to to is find a way to take the spectrum of those planets' atmospheres as they pass in front of their star. If we can do that, and we find that their atmospheres contain a lot of Oxygen, that would be almost certain proof of life.