what are the odds of getting consecutive cards in a deck after being shuffled?

Answer 1

Assuming that you don't care about suit and only denomination. Also assuming that both King and 2 are consecutive to an Ace.

Draw a card. There are then 8 other cards that would be consecutive, 4 above and 4 below. Since there are 51 cards remaining in the deck, the odds of getting a consecutive card would be 8 in 51 or about 15.7%

Answer 2

P(consecutive cards) =
(8*4+44*8)/(52*51) =
8*48/52/51
P = 0.1448
odds = (1-P)/P = 5.90625 to 1 against