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As others have alluded, MIDI data is the key to what you want. MIDI is essentially sheet music for computers, so you feed a virtual instrument that MIDI file, and it plays it for you. Most software even refers to the visualized MIDI data as the "piano roll."
You can see the little piano keys represented here, and the notes that will be played as the file is played through the selected instrument. There are numerous virtual representations of all kinds of piano.
The problem is making any kind of transcriptions of copy written songs is a legal grey area, and many sheet music and guitar tab sites get shut down.
The programs the others are discussing, turning mp3 straight to midi have issues because it's lumping the data for all the instruments (likely more than you realize, sometimes dozens per song when things are layered to sound bigger) into a single feed. All those instruments interplay with each other differently harmonically, and are played with different techniques. A piano is played differently than an organ, let alone something like a trumpet, so the software doesn't know how to filter what is trying to be created artistically.
So you can do it and it's relatively straightforward, but not something you're going to do on the fly is in a legal grey area.
I can go into any of this more if you want deeper explanations.