A game is played with a deck of ten cards numbered from 1 to 10. Shuffle the deck thoroughly. Take the top card. If it is numbered one, you win. If it in numbered k, where k>1, then replace the card into the kth positition from the top and draw again. You are allowed a maximum of 3 draws before losing the game. What is the probability of winning?
After the 1/10 chance on the first draw, I no longer know how to solve.