Q: Probability of drawing three different suits with a joker included in a single deck. I found here how to calculate the probability of drawing three cards from a standard 52 card deck and have all three be different suits.
It's $39/51⋅26/50=169/425$ which is 0.397647...
If a joker was added to the deck would I simple add one to the denominators in the above equation or do I subtract the probability of drawing the joker from the result above?
I plan on working on similar problems so is there a good book/PDF/link one may provide that deals with these types of card combination probabilities?

A: There are 13 cards of each suit in a 52-card deck.
If you add a joker, then there are still 13 cards of each suit in a deck, but the deck is now 53 cards.
Therefore the probability of drawing three differently suited cards is:
$$1 \cdot 39/52 \cdot 26/51 \approx 37.5\%$$
So your intuition that you just add one to the denominator is correct.
