In one of the old Microsoft solitaire games where you could enter the game number, there were a few negative game numbers that would give special deals. IIRC, one of those put the aces on the bottoms of four of the piles, kings and jacks on the top, and queens and tens under the K and J. It didn’t matter what was in your draw pile or if you drew 1 or 3, there were no moves possible.
The same stalemate could be obtained with 2s and 4s on top and A and 3s under them, or a variety of similar deals.
I’ve never seen one from a random shuffle, though.
According to this estimate, the chance of an unplayable game when drawing three is about 1 in 400. It’s not something that can be easily calculated, so the author used a Monte Carlo simulation to determine the odds.
I’ve had this happen to me a few times on the Microsoft version (playing draw 3) and must have played a few thousand hands, so that tallies with my experience.