How to play a melody by ear
/"You guys, what's that bit that comes after, 'Well, I'm not the world's most physical guy..." (Cornell University Library)
If you'd like to be able to play piano by ear, you need to train your fingers to play what they "hear."
No one thinks it's all that amazing to be able to hear a tune and sing it back accurately - it's just what the muscles that control your voice are trained to do. Over time, your fingers will gain enough experience to do this as well.