What does "nose out" mean?

Defeat by a narrow margin, as in She barely nosed out the incumbent. This expression, alluding to a horse's winning with its nose in front, has been used figuratively since the mid-1900s.

Discover, especially something hidden or secret, as in This reporter has a knack for nosing out the truth. This usage alludes to following the scent of something. [Early 1600s]