Loosely speaking, detectives may solves a case with two types of useful tools, intuition and facts. While facts are limited and confined to the current case on hand, intuition draws from a detective’s previous case experiences and established criminal profiles, which may not be related to the current case at all. A good detective, such as Sherlock, is able to combine both to form a fact-based and yet coherent theory to crack the case. In other words, the facts fit the intuition and together they reveal the truth.
However, in this case, intuition and facts were telling different stories. Mary’s good temperament and sterling reputation made her seemly innocent. In contrast, Author’s character and dubious behaviors made him an apparent suspect. These were simple intuitions drawn by almost everyone in the case, and were partially supported by some of the facts, such as Author holding the coronet at the crime scene and refusing to tell what he had seen or done. But there were also other facts in this case that run counter to these intuition, especially the footprints in the snow suggesting otherwise. Most people were willing to accept the hypothesis mostly guided by intuition, despite some conflicting facts, but not Sherlock Holmes.
For Sherlock, intuition, no matter how useful and confirming, is fundamentally not pertinent to a case. Intuition should never be used as direct evidence in solving a case. Rather, it is a pattern recognition and fitting process to organize and interpret the facts on hand. Facts, on the other hand, no matter how small and trivial, are direct and pertinent evidence, and should always be prioritized over intuition. In other words, if intuition does not fit all the facts, a detective should rely on the facts and adjust his/her intuition, or even abandon it all together.
Psychologically, confirmation bias comes natural to human. Being fact-based and not fooled by intuition is important not only in solving a criminal case, but equally in forming correct opinions and conclusions in everyday life.