I wonder how likely it is that this sort of thing happens without a mic being involved. Consider that Facebook already mines all sorts of Facebook data, as well

I wonder how likely it is that this sort of thing happens without a mic being involved. Consider that Facebook already mines all sorts of Facebook data, as well as data from websites you visit. They much have a pretty good profile of people's interests. Given that, it's fairly probably that you will be shown ads about things that you are interested in, and it's fairly probably that you'll talk about these topics with friends. Given this and the number of people that use Facebook, it's probably not that unlikely that your experience happens simply by chance fairly frequently.