The Brooklyn-born Hall of Fame trainer will be looking for his third win in six years in the $1 million Belmont Stakes today, and he has two of the three favorites for the final leg of the Triple Crown.

Ice Box, the Florida Derby winner who staged a tremendous rally to finish second in the Kentucky Derby, is the 3-1 morning-line choice. Fly Down, who blew away the field by 6 lengths in winning the Dwyer last month, is the 9-2 third choice.

The 142d running of the Belmont may lack Derby winner Super Saver and Preakness winner Lookin At Lucky, but Zito says the Belmont is, well, the Belmont.

“It’s big,’’ he said. “It’s a classic race. It’s the Belmont.’’

Zito’s pair tops a field of 12 3-year-old colts and geldings who will try to ace racing’s “Test of the Champion,’’ a 1 1/2-mile lap around Belmont Park in the longest of the Triple Crown races.

“It’s a tricky kind of race,’’ Zito said. “Our horses are fine with the distance, we just want to see if they kick in. You have to fire at the right time, too.’’

First Dude poses a huge threat as the 7-2 second choice. Probably the biggest horse in the field — he stands 17 hands tall — the colt trained by Dale Romans is coming off a gallant runner-up effort in the Preakness.

“The Belmont will be this horse’s race because he wants to go a mile and a half,’’ Romans said, “and he’ll love the track.’’

First Dude, along with Game On Dude and Uptowncharlybrown, are candidates to set the pace, while Zito’s colts have a similar come-from-behind style.

A hot and muggy day is forecast, with temperatures in the 80s and a 50 percent chance of thunderstorms.

The rest of the Belmont field is filled with long shots, but don’t discount the chances of 10-1 shots Game On Dude, Make Music for Me, and Uptowncharlybrown.

Lone Star Derby winner Game On Dude is trained by Bob Baffert, who saw his three Triple Crown attempts fall short in the Belmont but owns a Belmont with Point Given in 2001.

“It’s sort of wide open,’’ Baffert says. “We’re all within 5 lengths of each other. It’s whoever can go the mile and a half, that’s what it comes down to.’’

As Fly Down’s jockey John Velazquez said: “This track can be very deceiving. You have to know where you are. Sometimes it isn’t easy. And you have to have a good horse who can run that far.’’