Dependent event: Were you to start with a deck of cards and draw 1 card at random. Suppose you've drawn the king of hearts. You don't replace this card. What are the chances that your next draw will be another heart? Because you have not replaced the king of hearts, there are 12 hearts left, out of 51 (not 52) cards. Your chances of drawing another heart are therefore 12/51.
Independent event: You draw the Queen of Diamonds from your deck. Then you replace this card and shuffle the deck. Your chances of drawing the Queen of Hearts again is the same as before: 13 out of 52, since there are 13 hearts in the 52-card deck.