However, Facebook has a long history of changing their privacy policy and settings, and always in a way that (by default) makes public some things that previously were private. Usually with a couple of weeks to a month notice, not more.
So, unless you are diligent enough to review/delete your private stuff every time Facebook makes such a change, it is likely that in the future, stuff you marked "private" today will, in fact, be publicly indexed and searchable by yandex tomorrow.
Which is why, as has always been the case, you should assume everything you do on Facebook is public. Either because Facebook will decide to make it that way one day; or because of a security breach of some sort (hasn't happened yet, as far as I know), or because NSA/MI5/Mossad has access to it and will use it against you at the most inopportune moment (for you; it's a great moment for them).