The chances of Joe Arpaio winning the U.S. Senate race in Arizona are so absurd, according to a local pollster, that it is more likely voters will come across a photo of the former Maricopa County sheriff sporting the line of pink underwear he used to make inmates wear.

Mike Noble, chief pollster at the Phoenix-based OH Predictive Insights, said the survey he released Wednesday shows the GOP Senate race and the general election contests to replace retiring Republican Sen. Jeff Flake are tightening, but that the findings don’t bode well for Mr. Arpaio.

“We have a better chance of finding a photo of Sheriff Joe Arpaio wearing pink underwear and eating green bologna than to see him as the next elected senator of Arizona,” Mr. Noble said.

During his tenure at the Arizona jail, Mr. Arpaio was known for a tough on crime agenda that included the establishment of a tent city, serving inmates bologna sandwiches and making them wear pink get-ups.

Wednesday’s poll from OH Predictive Insights found that Rep. Martha McSally is leading the race for the GOP nomination thanks to the support of 35 percent of likely voters.

Former state Sen. Kelli Ward is running second with 27 percent, followed by Mr. Arpaio who has 15 percent. Twenty-three percents of the respondents remained on the fence.

Last month, Mrs. McSally held a 14-point lead in the same poll and Mrs. Ward trailed by a wider margin.

“While this is clearly an edge, the presence of hardcore conservative Sheriff Joe Arapio is playing spoiler to a potential Ward candidacy,” the poll analysis said.

Democratic Rep. Kyrsten Sinema is leading the three GOP candidates in hypothetical general election matchups, the poll said.

Ms. Sinema leads Mrs. McSally by 4 percentage points in a potential general election matchup. Mrs. Ward trails the Democrat by 10 percentage points, while Mr. Arpaio trails by 18 percentage points.

The GOP poll included 576 respondents via live and automated phone calls of likely voters and has a margin of error of 4 percentage points.

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