As of Wednesday afternoon, he had received more than 63 percent of the vote.

Mr. Hof had previously run for State Assembly as a libertarian in 2016. It was his first run at public office, Mr. Muth said, and he lost to the incumbent, James Oscarson. In June, Mr. Hof defeated Mr. Oscarson in the Republican primary.

Mr. Hof was born in Phoenix on Oct. 14, 1946, according to his website. His first job was delivering newspapers, and he later pumped gas. He went on to open several gas stations of his own, first in Arizona and then in Nevada, before entering the brothel business.

When he died, Mr. Hof had gained a national reputation as an outspoken supporter of brothels in Nevada, the only state in the country where they are legal in some counties. Nye County said in a report this year that in 2016 and 2017, brothels generated more than $392,000 for the county, offset by costs of just over $31,000.

In a 2012 interview with Channel 4 News in Britain, Mr. Hof said that if prostitution were illegal, it would be run by criminals instead of being safe and regulated in a legal sphere. Mr. Hof was the star of the HBO television series “Cathouse,” which focused on the Moonlite BunnyRanch, his brothel east of Carson City.

In 2015, the former N.B.A. player Lamar Odom was hospitalized after he was found unconscious at one of Mr. Hof’s brothels.

In April, two women told The Las Vegas Review-Journal that Mr. Hof had sexually assaulted them. One of them, Jennifer O’Kane, said that he put his hands around her throat one night in 2011, told her she “was his” and raped her, and that she was “raped and battered daily” by Mr. Hof.

Mr. Hof denied the claims, telling The Review-Journal that they were “muckraking in the political cesspool that keeps so many good people from running for office.”