Sometimes, when I'm watching any TV show which has a live hired band for accompanying and they have a musician guest, the host will ask for them to sing something on spot (that wasn't really planned), and they'll say to the band "please give me C Major [or whatever key]". Then they'll start singing and the band will typically join him/her after a few notes. How do these guys figure out the entire chord progression for the song instantly? (I'm obviously interested in situations like this that aren't staged.)

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