Joe Arpaio, the infamous former sheriff of Maricopa County, Ariz., announced on Tuesday that he is running for the Senate seat soon to be left open by retiring Republican senator Jeff Flake. Before Arpaio entered the race, the dynamics of the GOP primary seemed straightforward enough: In the populist lane was Kelli Ward, who enjoyed endorsements from the likes of Steve Bannon and Sean Hannity; Representative Martha McSally was set to fill the other lane, earning the support of Mitch McConnell and his political allies. If a third candidate entered, it was expected to be former state GOP chairman...