Belmont Park’s clubhouse, grandstand and hospitality areas seat 27,000, leaving 63,000 general-admission tickets under the cap. For the first time since 2005, the price of general grandstand admission was raised, to $15 from $10. The prices of about 1,000 grandstand seats were reduced slightly from 2014.

The last time a horse swept the Triple Crown — Affirmed in 1978 — 65,417 were on hand at Belmont. In perhaps the most thrilling Belmont Stakes of all, Secretariat won by 31 lengths in 1973 to capture the Triple Crown in front of a then-record crowd of 69,138. But as the Triple Crown drought has grown, attendance at Belmont with a Triple Crown on the line has soared, along with attendant problems.

Indeed, this year’s Preakness served as a reminder of what can go wrong when a huge crowd attends an event on a hot day. In the late afternoon, several toilets stopped working, leading to some unrest at Pimlico Race Course. Track officials initially said the cause was a water main break about two miles away, but after the event, the Baltimore Department of Public Works determined that the cause had been heavy use, aggravated by the use of a fire hydrant to fill the track’s water trucks.

A similar restroom water-pressure problem occurred at Belmont Park in 2008, when 94,476 looked on as Big Brown failed in his Triple Crown bid on a hot day, leading some guests to use stairwells to relieve themselves.

Sal Sinatra, vice president and general manger of the Maryland Jockey Club, said that while he was against limiting attendance at Triple Crown events — “Heck, I’m trying to fit 150,000 people here,” he said — he understood NYRA’s concerns.

“If you have a smaller venue, you have no choice, but Belmont can handle the people,” said Sinatra, who was stuck in the parking lot for hours at last year’s Belmont and saw fights break out. “But if you run out of something, like water, you’re going to get criticized.”