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There will be two cases:

Case 1: One spade(but non-king) and 1 king : 12C* 4C

Case 2: One spade(But King) :(only one king of spade is there) : 1C1    and 1 more king : 3C1

Now total probability required : ( 12C* 4C1  1C1 *3C1) /  52C2    =  1/26 .

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