Katy Perry's new album features a track titled "Ghost." In Season 1 of Ke$ha's reality TV series 'My Crazy Beautiful Life,' the instrumental for "Ghost" is played on the season finale.
Skip to 12:00 and you'll start hearing the instrumental in the background shortly.
It was an unreleased/unused track, so how exactly did she copy? Dr Luke probably just gave the instrumentals to Katy since Ke$ha never released it. It happens all the time in music.