[Update: El Chapo was sentenced to life in prison.]

In the coming months, as the infamous drug lord Joaquín Guzmán Loera is finally sentenced and put behind bars, his American jailers will confront a question that long bedeviled their counterparts in Mexico: Given Mr. Guzmán’s Houdini-like talent for breaking out of prison — a trick he pulled off twice — where, and under what conditions, should he be incarcerated?

Ultimately, prison officials will make that decision, but lawyers for the kingpin known as El Chapo warned him after his conviction this week on drug conspiracy charges that he is likely to be sent to the country’s most forbidding federal lockup, the United States Penitentiary Administrative Maximum Facility in Florence, Colo., often referred to as the ADX. More colloquially known as the Alcatraz of the Rockies, the ADX was meant to be both punitive and escape-proof, a penal fortress where inmates spend 23 hours a day inside their cells with little human contact and only one window, three feet high and four inches wide.

“This place is not designed for humanity,” Robert Hood, a former warden, once told The New York Times. “It’s not designed for rehabilitation. Period. End of story.”

Opened in 1994 on a barren stretch of semiarid desert 40 miles south of Colorado Springs, the ADX for decades has served as the final destination for a roll call of prominent criminals.