Making inferences

Here is a deal from Marshall Miles's book All Fifty-Two Cards (p. 26), an interesting guide to reading what's in the other players' hands.

West	North	East	South
1	Dbl	Pass	2
Pass	4	Pass	Pass
Pass

Lead:  K

North

 A Q 8 5

 Q 10 8 6

 7 5

 A Q 6

South

 J 7 4 3 2

 A J 3

 A 6 3

 8 4

West leads the king of diamonds. Sitting South, how do you approach the hand? There are three finesses that you can take. Can you improve your odds?

Updated with hint: You're wondering where all the kings are. West's king lead means he has the diamond queen as well. That's 5 points; his opening bid promises ~13 points, so maybe he has all three other kings. At minimum, he's got to have two of them.

How do you play the hand to maximize your chance of success, given the knowledge that East has either one king or no king? Try on all the possibilities in your mind. Please show your work for full credit.