Step 1: Understand the total number of cards.
In a standard deck of 52 playing cards, there are 4 kings. The total number of non-king cards is 52 - 4 = 48.
Step 2: Calculate the odds.
The odds in favour of drawing a king are the ratio of the number of kings to the number of non-kings:
\[
\frac{4}{48} = \frac{1}{12}.
\]
Step 3: Conclusion.
Thus, the odds in favour of drawing a king are 1:12, corresponding to option (A).