With a second, non-ace pile, repeat the process of moving three cards to the bottom and dealing a single card on each of the other piles
Repeat with the third (last) non-ace pile.
Before proceeding to the final step and reveal, let's review the position of the cards in each pile. Three piles (the "non-ace" piles) have a mix of random cards. We are not interested in these piles.
The pile with the aces has three random cards on top, which is followed by the four aces.
When the spectator does the same mixing process in the next step, the three random cards will be sent to the bottom of the pile, and then one of three aces will be dealt to the top of each of the other piles. One ace will remain on top of the "ace" pile.