Finding Explanations That Make the Campaign Better
Examples of abductive reasoning in RPGs abound. For example, in my Classic Dungeons & Dragons campaign, my party of adventurers has been exploring another world in their crystal sphere, filled with strange and alien beings. To fill up this new setting I have been liberally adapting unused encounters and dungeons for use in the new world. One such encounter was an ettin in a jail cell. Ettins are common enough in the Auran Empire from whence the adventurers hailed, but were not a creature that was native to the alien world they were now on.
Now, outside of the context of the game, the reason an ettin might appear is simply that he had been created for a different dungeon in a different campaign, where his presence would not have been surprising. But on the alien world, his presence was odd indeed and demanded justification or removal. I could have simply changed the ettin into another creature more appropriate to the new world. But I didn't - instead, I abduced why an ettin might be present.
So, the surprising fact: An ettin on an alien world.
My abduction: If there was a strange portal through space and time that swept up creatures from the Auran Empire and deposited them on the alien planet, the presence of an ettin would be a matter of course.
My conclusion: There is reason to suspect that a mysterious gate through spacetime exists on the alien world.
By simply importing a legacy encounter from an old dungeon I had laying around, I have suddenly concluded that a mysterious portal exists somewhere that brings in creatures from the old world to the new. If I had simply changed the ettin into an alien, this portal would not have existed, and the game world would be a less interesting place.
Note that I did not start with the idea of the portal - I started with the arbitrary appearance of the creature. This is not cause-effect reasoning; it's the opposite. It's finding an explanation for something that didn't have one - an explanation that made the campaign better.