Re: It's not just a big distance to cross... there's a lot of history
Pretty high - life started on Earth (and effectively the universe) pretty much as soon as was practically possible. Very broad stroke, but in terms of the universe forming and going through the various stages of element creation through the various stars up to Population I stars (like ours) and a surrounding solar system, the formation of the earth, life started pretty much (in astronomical terms) as soon as the conditions were right.
If we assume the rest of the Population I stars underwent a similar cycle (and no reason to doubt they didn't) makes it extremely likely that life would start on similar timescales across the universe.
In short, for a lot of history across the universe, life wasn't possible. And even without that, we know that life on Earth has existed for about 1/6 of the universe's life.