I say all this not having seen the production, as I said, though I did read the book it's based on, Arthur & George. The book is a novel, but it's based on a true story. George is the son of a vicar in Victorian England who is an Indian solicitor insisting his life was ruined by being wrongly convicted of the mutilation of horses and threatening children, and Arthur (which is the great fun and twist of this piece) is none other than the creator of Sherlock Holmes -- Sir Arthur Conan Doyle.
As you might imagine, Doyle wants no part of this, being an author not an actual detective, and also he's still recovering from the loss of his wife, but it's the persistence of George that eventually gets him involved in investigating the mystery.
The book by Julian Barnes was shortlisted for the Man Booker Prize. (And earlier version of this article said that it had won. I was properly and gratefully informed of the correction.) It's not terribly long and much easier reading more more accessible than most Booker Prize-winners I've read. I didn't deeply love it, but it was nonetheless very enjoyable, and thoroughly fascinating.
Also recommending the film production is that Conan Doyle is played by the wonderful Martin Clunes, who stars in the terrific British series, Doc Martin.
As I said, if you missed the first episode, PBS posts their shows online, and you can catch it by clicking here. The episode only runs 46 minutes (including introduction and "coming next time"). I'm guessing that this was done as simply a "one-off" standalone 2-hour TV movie in England which they've broke up into three parts here for Masterpiece Mystery.
And below is a trailer preview that they ran in England.