I think you are right that science fiction is not "a rational attempt at analysis" but that you are wrong that it is usually "because stories don't use probability distributions." Some time ago, I tried writing a story using the RPG Exalted's rules. Keeping track of such a large number of character sheets turned out to be too tedious, and I gave up. Yet, the point was to make the story more surprising, not more realistic. If I write "With 45% probability, Vash dodged the bullet fired at him at point-blank range, and with 10% probability, he dodged a sniper shot taken from seven miles away" this is not unrealistic because it doesn't use probability; rather, it isn't even an attempt to be realistic, or to rationally examine what the future might be like.
It's also possible to be hit by this bias if you're not thinking of it while shopping. Last year, I was invited over to watch the Super Bowl at a friend's, and they were also celebrating his niece's birthday. Of course, I brought a gift -- a Cookie Monster plushie. Unfortunately for me, someone else brought a teddy bear that was obviously much larger and higher quality! Oops.
The moral, I suppose, is that if you're going to get a cheaper gift, shoot for something that's very different than what other people are likely to buy.