March 15, 2015 9:42 PM EDT

It almost sounded like a confession.

At the end of Robert Durst’s final interview for the HBO docuseries The Jinx, he heads into the bathroom while fully miked. Seemingly unaware that he was being recorded, he talked to himself. “You’re caught,” he mumbled. “You’re right, of course. But, you can’t imagine. Arrest him.”

“What the hell did I do?” he continued. “Killed them all, of course.”

It’s unclear whether this was a confession, but the FBI did arrest Durst on Saturday afternoon in New Orleans. (The FBI had been investigating Durst apart from the documentary and there’s no evidence that they arrested him because of his confession on Sunday’s episode.)

The arrest may have come at the right time. Durst seemingly had all the tools for a clean getaway.

According to a law enforcement source familiar with the investigation, Durst had checked into a Mariott in New Orleans under a false name. In his possession, according to the source: a fake passport, other falsified documents, and a large amount of cash.

“It was obvious that he planned to get the hell out of Dodge,” says the law enforcement source, noting that Durst was arrested on a capital murder warrant. “It was the first day that the New Orleans airport was offering flights to Cuba, so that’s where we think he was going.”

Durst, 71, is accused of killing his friend Susan Berman, who was found shot execution-style in her California home in 2000.

It’s not Durst’s only brush with the law. He has widely been suspected in the 1982 disappearance of his wife Kathleen. In 2001, he was arrested for the murder and dismemberment of neighbor Morris Black. He was later acquitted.

Detective Cody Cazalas, who investigated the murder of Black, tells PEOPLE that he was “ecstatic” at the news of Durst’s arrest.

“When we were investigating the murder of Morris Black, we always thought that he had something to do with the murder of Susan Berman,” says Cazalas. “She said she was going to talk to investigators about him, and then right before she could, she was murdered. He was always a person of interest.”

It doesn’t matter to me whether he’s arrested in Los Angeles, New York, Texas, if the FBI arrests him, whatever,” continues Cazalas. “All that matters is that he’s off the street, because he’s dangerous. He looks like an old, frail man now, and I get that. But you don’t have to be strong to pull a trigger.”

A friend of Kathleen Durst shared a similar sentiment. “I’m relieved,” she tells PEOPLE. “Very relieved.”

Durst’s estrange brother agrees. “We are relieved and also grateful to everyone who assisted in the arrest of Robert Durst,” Douglas Durst said in a statement. “We hope he will finally be held accountable for all he has done.”

With additional reporting by Michael Miller

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