I will assume that the defenders know South has a singleton, and further that each defender knows that the other defender knows that South has a singleton.
Case A, West plays the
King.
West has a one card suit
1. West has K singleton. We are cooked in this case so ignore this one.
West has a two card suit.
2. West has KQ tight. Here, take the Ace and lead low is a winner.
3. West has KT tight. Here, take the Ace and lead the Jack is a winner. If West plays the ten, North will cover with the Jack, and whether East takes his Queen or ducks, declarer will succeed. So the King is a much better play by West.
4. West has Kx. If you win the Ace, you are cooked because East will play small and retains QT behind your J9. If you duck your Ace, no better. Either way you are cooked so ignore this one as well.
West has a three card suit.
5. West has KQx. Here, win the Ace and lead the Jack is a winner. East has Tx. But West has made a pretty bad play to split here, as South was going to play the 8 from dummy. But, if West plays low and South then plays the
Jack, then Ace and small, South has succeeded, so it’s not all that bad a play to split.
6. West has KTx. Here, win the Ace and small from the board is a winner. East has Qx in this case. West has made a very bad play to rise with the King here – so bad that no one would do it.
7. West has KQT. If you win the Ace, you are cooked and if you duck, no better. So ignore this one as well.
West has a four card suit.
8. West has any four card suit – then we are cooked. Even if West has KTxx and East the stiff Q, and West plays the K the first time (Crash!), you can only take 2 tricks.
So 3 is more likely than 2 (Restricted Choice), and 5 is more likely than 6. Therefore, play the Ace and lead the Jack is favored.
This makes my head hurt too much

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