Answer:
This is a very strange question because how would you know if a card drawn from a standard deck was black unless someone looked at it? And if they did look at it, they would know whether or not it was a king.
Let's assume that you have someone discretely look at the chosen card and simple tell you whether or not it was black, without disclosing the rank. This would continue until a black card was chosen. This shouldn't take too long since half of the cards in a standard deck are black, yielding a 1 and 2 change on each choosing, assuming replacement after each draw. But then, wouldn't it make more sense to simple remove all the red cards and blindly choose one of the remaining 26 black cards?
In any event, there are 4 kings in a standard deck of 52 cards. The odds would be 4 in 52 of drawing a king. Now, if you knew for sure that the card was black, the odds are equivalent to if you had blindly chosen a card from the 26 black cards.
Since there are only 2 black kings, the probability would be 2 in 26, which reduces to 1 in 13.
Step-by-step explanation:
