Would the Wizards take me at No. 1? (AP Photo/Nick Wass) Would the Wizards take me at No. 1? (Nick Wass/Associated Press)

The Wizards’ odds of winning the NBA draft lottery on Tuesday are slim and the actual prize isn’t obvious, since no player has distinguished himself as the unquestioned No. 1 overall pick. That doesn’t mean there won’t be any intrigue on the night Ping-Pong balls set the fate for non-playoff teams.

Washington will either end up with one of the top three picks or any slot between eight and 11, giving the team plenty of possibilities — and at least a dozen players to consider. A Wizards contingent that included team president Ernie Grunfeld and Coach Randy Wittman interviewed 15 players last week in Chicago at the NBA draft combine, but didn’t speak to the favorites to go first or second — Kentucky freshman center Nerlens Noel or Kansas freshman guard Ben McLemore — or UNLV forward Anthony Bennett, who didn’t attend because of left shoulder surgery.

The Wizards have a 3.5 percent chance of winning the top choice for the second time in four years, a 4.1 percent chance of picking second and a 4.8 percent chance of getting the third pick. If no team leapfrogs the Wizards into the top three — the most likely scenario at 70.3 percent — they will pick eighth. They have a 16.5 percent chance of picking ninth, a 0.8 percent chance of picking tenth and a 0.01 percent chance of being jumped by three teams and picking 11th.

Between now and the June 27 draft at Barclays Center, the Wizards will spend time observing prospects through workouts and dinners, field and make calls about potential trades and decide the best course of action for the organization. The day after the lottery, the Wizards’ brass will attend a two-day workout session in New Jersey for about 44 draft prospects hosted by Brooklyn, Houston and the Los Angeles Clippers. And next week, it will head to Minnesota for another workout hosted by the Timberwolves.

The Wizards will begin hosting players for individual workouts at Verizon Center beginning in June.

Grunfeld hasn’t ruled out trading the pick, but could be convinced to keep it, depending on which players are available wherever they wind up picking. The team will look to add more size, or possibly find a perimeter scoring option off the bench. One of those needs could easily be addressed with a top 10 pick.

Players available at one to three: Noel. McLemore. Bennett. Georgetown small forward Otto Porter. Michigan point guard Trey Burke. Indiana swingman Victor Oladipo.

The Wizards’ options: Emeka Okafor will be a free agent after next season and Nene missed 21 games last season as he dealt with an assortment of injuries, most notably the plantar fasciitis that has limited him for most of his time in Washington. If the Wizards are fortunate enough to win the lottery, the 7-foot Noel could be a solid selection though he is sidelined with a torn anterior cruciate ligament and probably won’t be ready to make his debut until around Christmas. Noel is a project, but would also have several months to bulk up after weighing in at a feathery-light 206 pounds at the combine.

Porter could be a viable alternative for the top spot and especially at two or three, since he could probably make an immediate contribution as a playmaker and wing defender. The 6-8 Porter already has a relationship with Bradley Beal and his versatility could provide insurance if the Wizards are unable to retain Martell Webster in free agency.

Bennett, a bruising power forward, is arguably the most skilled scoring big man in the draft, but is a tad undersized at 6-8. Oladipo is a tremendous athlete who improved each season in college and might still have another level to rise.

The Wizards already have their starting backcourt set with John Wall and Bradley Beal, which would make using a high pick on Burke or McLemore redundant.

Will I really be here at No. 8 or lower? (Photo by Toni L. Sandys/The Washington Post) Will I really be here at No. 8 or lower? (Toni L. Sandys/The Washington Post)

Players likely to be available between eight and 11: Maryland center Alex Len. Indiana center Cody Zeller. Gonzaga center Kelly Olynyk. UCLA swingman Shabazz Muhammad. Lehigh guard C.J. McCollum. Syracuse guard Michael Carter-Williams. Pittsburgh center Steven Adams. Duke center Mason Plumlee.

The Wizards’ options: If Len is available at No. 8, the Wizards would have a hard time passing on a 7-foot-1 big man with tremendous potential and an already solid foundation. Len could slide out of the top five after recently having ankle surgery, but unlike their previous picks from Europe (Oleksiy Pechorov — a Ukrainian native like Len — and Jan Vesely), the Maryland sophomore won’t have to adjust to the language and cultural barriers.

Zeller was considered a candidate for the top overall pick when the college basketball season began and helped his stock considerably at the draft combine, where he scored well in athletic testing and measured in at 7-feet. He has the ability to run the floor and knock down the open mid-range jumper, which should create space for Beal and Wall.

Olynyk and Plumlee would be the choice if the Wizards elect to go with dependable players who are capable of contributing immediately, but might lack much upside. Adams might be a reach for the top 10, but the New Zealand native’s ability to rebound and developing skills could be difficult to resist.

Even with Wall and Beal, the Wizards could make room for a talent like McCollum. The 6-3 combo guard is an electrifying scorer who would flourish in an uptempo system. McCollum also connected on 51.6 percent of his three-point attempts, which could make him a quality backup for Wall or a possible option in three-guard sets.

Muhammad was a polarizing figure in his one season of college basketball, but the 6-6 swingman has the ability to score and should enter the league with a tremendous chip on his shoulder. Carter-Williams didn’t have the individual success that he had hoped for, but his leadership was essential in helping the Orange advance to the Final Four.