The House Ethics Committee is probing whether Rep. Matt Gaetz, R-Fla., gave special privileges and favors to friends and obstructed a government investigation into his conduct, the panel said Tuesday in a rare public statement—a day after Gaetz claimed he faces a new “frivolous” probe. The committee said it has closed its probes into allegations that Gaetz shared inappropriate images or videos on the House floor, misused state identification records, converted campaign funds to personal use...