Zion Williamson #1 of the Duke Blue Devils celebrates a...

Zion Williamson #1 of the Duke Blue Devils celebrates a basket against the Virginia Tech Hokies during the first half in the East Regional game of the 2019 NCAA Men's Basketball Tournament at Capital One Arena on March 29, 2019 in Washington, DC.  Credit: Getty Images/Patrick Smith

As the Knicks stumbled through a 17-65 season, the worst record in the NBA this season and tied for the worst record in franchise history, at least the light at the end of the tunnel was the NBA Draft Lottery.

But when Tuesday’s lottery is held at 8:30 p.m. at the Hilton Chicago, the Knicks’ best odds are to land the fifth pick, thanks to a revamped lottery system that tries to dissuade teams from tanking and attempting to secure a slot at the top of the draft.

The Knicks have a 14 percent chance of landing the top pick, which almost certainly will be Duke’s Zion Williamson. That’s the same odds owned by the second- and third-worst teams, the Cavaliers and Suns, thanks to the system approved in 2017 by the league’s Board of Governors. This system, which will be implemented for the first time, has been swapped for a system that would have given the worst team a 25 percent chance at the No. 1 pick.

The Knicks have a 47.9 percent chance of landing the fifth pick. By virtue of having the worst record, they can’t slip below No. 5.

The Knicks’ odds for the rest of those five spots are 13.4 percent for the second pick, 12.7 for No. 3 and 11.9 for No. 4.

The last time the Knicks were 17-65, they had the second-worst record, but the 2015 lottery dropped them from the No. 2 pick to No. 4, with the 76ers and Lakers jumping over them.

It worked out as Kristaps Porzingis fell into their laps, or at least it did until the relationship between the Knicks and the franchise centerpiece splintered and they traded him to Dallas. That left the Knicks without a star, but it did create enough cap space for them to chase two max-salary stars this summer.

Patrick Ewing — the last player to lead the Knicks to regular contention — will represent the franchise on the dais Tuesday.

He was selected with the No. 1 overall pick by the Knicks in 1985 after the team won the first lottery, one that still is the subject of nearly as many conspiracy theories as UFO sightings are.

Was it a frozen envelope or a bent corner that allowed Ewing to land at Madison Square Garden?

The NBA has moved steadily to avoid those sorts of questions. Now, before the cards are turned over on the stage Tuesday night, the actual lottery will be held in a separate room with media members, NBA officials, representatives of the participating teams and the accounting firm of Ernst and Young in attendance.

Fourteen carefully tested and weighed Ping-Pong balls numbered 1 through 14 will be placed in a lottery machine. There are 1,001 possible combinations when four balls of the 14 are drawn, without regard to their order of selection. Before the lottery, 1,000 of those 1,001 combinations will be assigned to the 14 participating lottery teams.

Allan Houston will represent the Knicks in the room where the Ping-Pong balls are drawn. “There’s no such thing as luck,” he said. “You know that.”

And that’s hard to argue concerning the Knicks, who have rarely seen anything but hard times since Ewing departed.

Chances are

Teams in the draft lottery and their chance of winning it:

Team Odds

New York 14%

Cleveland 14%

Phoenix 14%

Chicago 12%

Atlanta 10%

Washington 9%

New Orleans 6%

Memphis (a) 6%

Dallas (b) 6%

Minnesota 3%

Los Angeles 2%

Charlotte 1%

Miami 1%

Sacramento (c) 1%

a-Pick may be conveyed to Boston.

b-Pick may be conveyed to Atlanta.

c-Pick will be conveyed to Boston or to Philadelphia)

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