Probability of a Singleton King
You (South) are declaring; you lead the Jack from dummy and East follows low, in tempo.
How likely is it that West was dealt the singleton King? Missing five hearts, singleton King offside is only about 3%. But what if declarer has six hearts (EW have four)?
Now how likely is it that West was dealt the singleton King? Missing four hearts, only about 5%. Also, we point out that, with six hearts, declarer almost surely would not have rebid one notrump. And what if EW have only three hearts?
Now how likely is it that West was dealt the singleton King? Even missing three hearts, only about 13% (higher than before, but still not a strong chance).
When a strong declarer drops a singleton King offside, declarer is almost never guessing; rather, declarer probably has found a clue that the King is very likely to be behind the Ace (and thus there is very little reason to consider finessing), or declarer has reason to take two rounds of trumps immediately (and dropping the King is simply a bonus), or declarer can’t afford to use an entry to take the finesse (and dropping the King is simply a bonus).