The latest in the Hogarth series of contemporary retellings of Shakespeare’s work is unashamedly commercial. From the moody cover to the blurb boasting that this is the new thriller from the No 1 bestselling author, there is a determined attempt to drag this tale a million miles away from images of dusty theatres and tights. Only a brief statement by Nesbø that he sees the play as “a thriller about the struggle for power, set both in a gloomy, stormy, noir-like setting and in a dark, paranoid human mind” alludes to its origins. On its own terms, this is a “fair and foul” crime novel with a vivid sense of place that will please Nesbø fans. But as an adaptation of Macbeth, it encourages us to hope that it might be something more special. In this, alas, it proves a slight disappointment.

Nesbø sets his story in a grim and stormy industrial city in Scotland, where the murky weather is matched by the moral smog that its inhabitants fester under. Enter Duncan, the idealistic, upper-class chief commissioner, who vows to clean up the streets and promotes Swat commander Macbeth to the post of head of organised crime. On the face of it, Macbeth seems a perfect fit – an orphan and former drug addict, he has seen plenty of the dark side of humanity and yet remains untainted by it. But this is to overlook Macbeth’s glamorous partner, Lady, owner of the local casino; then there’s the shadowy Hecate, crime overlord and arch-manipulator. The narrative tallies closely with the play, though there are a few additions, not least a terrific set piece concerning a drugs bust gone wrong, which starts things off with an appropriate bang.

When Nesbø has the courage to move away from his source, the narrative and characters feel liberated

Although there’s nothing wrong with Nesbø rewriting the Scottish play as a police procedural not a million miles away from his Nesbø’s Harry Hole novels, it neither offers a contemporary response to its source nor entirely succeeds as a beat-for-beat update. There is a dearth of sympathetic characters (not that Macbeth is full of likable types), which means that it is often hard to care about the dark goings-on. At 500-odd pages, many readers may feel that they have got the point long before the inevitable, wordy confrontation between Macbeth and Macduff (here simply called Duff) finally arrives.

Nesbø’s prose, as efficiently translated by Don Bartlett, alternates between the matter-of-fact and uneasy attempts at Shakespearean grandeur and poetry; initially declining to participate in Duncan’s murder, Macbeth announces: “I won’t do it because I can’t find the will for such villainy… what’s the point, apart from feeding my ambition.” There are many explicit verbal references to the original, which range from the knowing and wryly amusing (Macbeth is an expert at throwing daggers, a legacy of a brief career in the circus) to the banal. “Bring forth men-children only,” did not need to be updated to “You can only give birth to boys, can’t you?”

Yet there are compensations. When Nesbø has the courage to move away from his source, the narrative and characters feel liberated. The decision to change Hecate from the leader of the witches into a Krug-sipping, aphorism-spouting eminence grise is a boldly effective transposition, and there’s a sharp subtext about the way in which class distinctions play their part in the world of policing that might even have turned into satire had it been pushed a few notches further.

Ultimately, this will appeal to Nesbø’s substantial and loyal readership and admirers of the Hogarth series who want to see how this notoriously tricky play has been tackled. It may be full of sound and fury, but this isn’t a tale told by an idiot.

• Macbeth by Jo Nesbø is published by Vintage (£20). To order a copy for £17 go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99