Going on the evidence we have, it's certainly not impossible that our own planet (one out of something like 10^25 likely planets in the universe) happens to be

Going on the evidence we have, it's certainly not impossible that our own planet (one out of something like 10^25 likely planets in the universe) happens to be the only one that life has arisen on, which I'd say qualifies as astronomical odds against for any random planet at least.