There’s nothing fancy about The ABC Murders, which arrives Friday on Amazon Prime. It’s just a bloody good murder mystery.

No surprise there. Agatha Christie wrote The ABC Murders, and Detective Hercule Poirot is played by John Malkovich. BBC One produced it.

So we have that rare instance where one might ask, “What could possibly go wrong?” and the answer is that nothing does.

Unspooling in three episodes, The ABC Murders revisits Poirot in retirement. And frankly, he’s slightly bored with it.

He’s drawn back to the game when he begins receiving anonymous letters from someone who knew his reputation from the old days and seems to derive a thrill from planting hints about murders he is about to commit, as if daring Poirot to locate and apprehend him.

Or, more likely, to be the criminal who was so clever that even the great Poirot could not stop him.

Our apparent suspect, however, is not a slick, suave, ostentatiously confident man of the world. Alexander Cust (Eamon Farren) seems to be a traveling salesman whose business, like many enterprises in 1933 Britain, is tenuous. He’s scrambling.

Poirot too faces obstacles. His long-time colleague Inspector Japp (Kevin McNally) has retired to take up gardening and the new bloke at police headquarters, Inspector Crome (Rupert Grint), holds Poirot in contempt.

While Crome’s reasons are unclear, the effect is not. Poirot tries to warn him of the pending murders and Crome dismisses Poirot as a washed-up old gumshoe who just wants to grab a last bit of glory.  

This has an impact on Poirot, who remains mildly troubled by the angst that marked his whole career. Malkovich conveys this psychological shadow beautifully, with the slightest facial movements and almost imperceptible gestures.

Poirot also retains all his detective skills, however, and it becomes clear he will need them. The clues he receives from the killer don’t yield enough information to head his crimes off, and the patterns don’t point to specific potential victims.

In keeping with Christie’s own patterns, those victims aren’t all choir boys and girls. We don’t wish them dead, necessarily, but we see that they have some flaws, which will at certain points provide Poirot with critical guidance.

So as we wonder how long the killer can stay ahead of the law, we also watch the dance of suspicion between Crome and Poirot – with the question being whether their single area of agreement, that they would like to catch the perp, will eventually bring them into some sort of uneasy alliance.

Writer Sarah Phelps has done a superb job of adapting Christie’s narration into a screenplay, a task that some recent productions confirm can be more difficult than it might seem.

She and director Alex Gabassi maintain the tension while sprinkling in little details and visuals that evoke Depression-era England. The dangerous social and political undercurrents of that time aren’t tossed in our faces, but at the moments when they matter, we understand their significance.

The ABC Murders is a fine antidote for cold winter nights.