What are my odds of drawing the rest of my deck
50%

Symbolizing the cards that give you a draw a D, and the cards that do not as N, there are 6 possible permutations of draw vs no-draw.

In each permutation, the second N card represents the farthest you can get through your deck on this turn.  I have bolded it for easier visibility.

DDNN

DNDN

DNND

NDDN

NDND

NNDD