Whenever George shops at the supermarket, he first writes his shopping list in a random order, and then always picks items off the shelf in the same order as his shopping list, regardless of their position in the aisles.
George arrives at the supermarket late on a Sunday afternoon to find that a one-way system has been implemented for the purposes of social distancing. If he wants to buy the next item on his list but has already walked past it, he cannot go back, but must instead proceed to the checkouts, buy whatever is currently in his basket, leave the supermarket, and re-enter it from the start.
George has seven items on his shopping list, but only has time to go through the supermarket one-way system three times before it closes. To four decimal places, what is the probability that he can buy everything on his list?