The idea of bigger-than-life characters playing mismatched investigators is nothing new to television. But those who didn’t pay attention in history class may be startled by the stance each figure takes in their cases, which largely revolve around the possibility of an afterlife. Arthur Conan Doyle, whose wife is in a coma, takes to seances the way Sherlock gravitated to morphine. Harry Houdini makes a side career out of debunking mediums and psychics.

Think “The X-Files” with only the slight thread of sexual tension.

“Doyle, who created the most skeptical character, was a believer in the paranormal, and Houdini, a magician, was the most skeptical person alive,” said co-creator David Titcher, who’s also responsible for “The Librarian” franchise on TNT. “It’s that irony that made me want to do the show in the first place.”

It’s a novel idea, though one that’s not terribly bothered by accuracy. While the show is set in 1901, the two actually didn’t meet until nearly 20 years later, and the notion that two of the most famous people on the planet could wander in and out of crime scenes without being mobbed by fans requires a high degree of disbelief. But never let logic get in the way of TV’s desire to find a new spin on “The Odd Couple.”

“They were sort of these huge celebrities and isolated, sort of, and they find each other as friends. But it’s contentious,” said Michael Weston, who plays Houdini with a nervous itchiness that suggests he’s continually trying to wrangle out of invisible handcuffs. “Their whole approach to life is different — this brash American who just sort of busts in rooms and declares mission accomplished. And [Doyle] is this intellectual mind who meticulously goes about doing his business. They clash on a lot, but they need each other’s respect, and they need each other’s friendship. Two sort of great minds going at figuring out a puzzle.”

In the first episode, the two butt heads on a murder at a nunnery where the chief suspect is a ghost; next week, they investigate a faith healer who may or may not have the ability to bring Doyle’s wife back to consciousness.

“Each episode has a real different flavor,” said Stephen Mangan, who plays Doyle with a hangdog disposition that will remind you of the oft neglected brother on “Everybody Loves Raymond.” “One might be a gothic horror story. Another one is a psychological thriller. And they really have their own individual flavor. It’s really, really surprising and wonderful, I think.”

One case that won’t surface anytime soon: The Mystery of the Severed Friendship.

In real life, Houdini accused Doyle’s wife of being a fraud, while Doyle labeled Houdini a dangerous enemy and, according to one historian, even plotted his murder. When will that level of animosity emerge?

“That’s Season 7,” Titcher said.