In the first scenario, you'll need to break it down into two separate events. Can you see why your scenario is equivalent to the probability of [(Red King) and (Another Red Card)] or [(Black King) and (Any Red Card)]? So, how many cards are in a deck? How many red kings are in the deck? Since there's only one of each card, any card is equally likely. What does that make the probability of drawing a red king? After you've drawn a red king, how many cards total are remaining in the deck? How many red cards? What does that make the probability of drawing one of those red cards? And what does that make the overall probability of drawing a red king then another red card?
Except now we have a problem. This only accounts for the specific scenario where the red king is drawn first. What if the red king is drawn second? If you go through the same train of thought as before, does that change the probability? What does that make the probability of drawing a (red king then red card) or (red card then red king)?
Now let's tackle the scenario where the king is black. We still can draw the king first or second, so we definitely have to do something to account for this, but can you see why we have a shortcut here because the probability is the same whether the black king is drawn first or second? What does that make the probability of drawing a (black king then red card) or (red card then red black king)? Finally, can you put everything together and figure out the overall probability of this scenario happening? If you can figure out the first scenario, the second one will be the same idea, only easier to work with.