(Oxford English Dictionary)
to win in a walk: to win easily and without effort. U.S. colloq.
1896 ADE Artie xii. 106 'Does he stand a good chance of being elected?' 'That's what keeps me guessin'. Two years ago he win in a walk [etc.].' 1903 A. H. LEWIS Boss 138 He won in a walk.
2 June 1867, New York Times, pg. 5:
At the recent meeting at Jerome Park she started and won twice; in the first race for three-year olds of three quarters of a mile, carrying 112 pounds, including 5 pounds extra, she fairly galloped away from her opponents, and "won in a walk."
4 August 1870, New York Times, pg. 8:
In both heats, Helmbold made the semblance of a race with him, but racing men well knew that the gallant chesnut was running under a hard pull, and could easily, if ROBINSON had given him his head, have come away by himself, and "won in a walk."
20 March 1897, Mountain Democrat (Placerville, CA), pg. 3:
NEW YORK SLANG.
Some of the Words and Phrases of the
Tenement House Folk.
Anything and everything that is done easily or quickly is said to be done "in a walk." Men are said to "get rich in a walk" or to win a boat race "in a walk." That is an expression borrowed from the turf, which has also lent to New York the word "ringer," perhaps the most difficult to explain of all the local slang terms, and yet, like all slang, most concise and expressive to all who make use of it. A "ringer," in slang, is anything that looks like what it is not; so that if a person is thought to closely resemble Grover Cleveland, he is spoken of as "a ringer on the president," or if he wears a brilliant bit of glass it is said to be "a dead ringer on a diamond." "Dead" signifies the utmost, the veriest, that which is absolute. -- Harper's Weekly.