I don't know the exact chance, but in my experience, out of 67 explored systems, less than 10% of them contained planets with ruins (which are discovered by geosurvey ships). While I believe they can appear in a reasonably wide range of environments, they tend to crop up on easily terraformable planets.
And so far, every ruin I've found has been guarded by Precursor contingents of various sizes. You can use such strength to gauge the size of the ruins themselves.