To be fair, it's possible that it's a real long lost Sherlock Holmes story by Sir Arthur Conan Doyle, it's just not very probable.
The story in question is 1,300 words in length and appeared in a 1903 pamphlet for a bazaar that was held to raise money for a bridge restoration in the town of Selkirk, Scotland. Sir Arthur Conan Doyle was a guest of honor at the bazaar, and provided some funding for the bridge restortation, but there's no mention of him writing a story for it. The pamphlet story is unsigned, and is most likely a part of a series of three "Notable Inerviews" written for the bazaar. The story opens with a nod to the previous two interviews, and it's terribly unlikely that Conan Doyle wrote those interviews as well. It's more likely that someone else wrote the story as a nod to Conan Doyle's attendance.
"Sherlock Holmes." — DISCOVERING THE BORDER BURGHS, and, BY DEDUCTION, the BRIG BAZAAR was found by historian Walter Elliot, who has apparently had it for 40-50 years, and brought it out of storage upon hearing that the bridge is to again be restored. You can read the text in full here.