Total number of cards = 52

Total Number of King Cards = 4

$\text{P[King] = }\dfrac{4}{52}$

Total Number of Diamond Cards = 13

$\text{P[Diamond] = }\dfrac{13}{52}$

Total Number of Cards which are both King and Diamond = 1

$\text{P[King and Diamond] = }\dfrac{1}{52}$

Here a card can be both a Diamond card and a King. Hence these are not mutually exclusive events.

[Reference : mutually exclusive events]. By Addition Theorem of Probability, we have

P[King or a Diamond] = P[King] + P[Diamond] – P[King and Diamond]

$= \dfrac{4}{52} + \dfrac{13}{52} – \dfrac{1}{52} = \dfrac{16}{52} = \dfrac{4}{13}$