The trouble with Holmes’ axiom is that it’s in direct opposition to Occam’s razor, which tends to be the answer more often than not. So one is likely to come to the improbable cause of an issue last, once all the simple causes have been tried and rejected. That’s probably the right way to do things, but it does slow things down in cases where time may be of the essence.
In other words, the only way to get to the improbable is by eliminating all that is likely yet impossible. There are no shortcuts.