The worst hand is the dreaded 1-2. It is composed of a high 6, low 6, low 4, and any 7. The probability of this hand is 2×2×2×4/combin(32,4) = 32/35,960 = 0.09%, or 1 in 1,124.
Interestingly, if the player played 0-3, the high hand would be a high-3, which is normally the minimum low hand the house way tries to achieve. I don’t know if that is a coincidence or not.