I'm talking about probability estimates. The actual probability of what happened is 1, because it is what happened. However, we don't know what happened, that's why we make a probability estimate in the first place!
Forcing yourself to commit to only one of two possibilities in the real world (which is what all of these analogies are supposed to tie back to), when there are a lot of initially low probability possibilities that are initially ignored (and rightly so), seems incredibly foolish.
Also, your analogy doesn't fit brazil84's murder example. What evidence does the lottery win give that allows us to adjust our probability estimate for how the gun was fired? I'm not sure where you're going with that, at all.
The real probability of however the bullet was fired is 100%. All we've been talking about are our probability estimates based on the limited evidence we have. They are necessarily incomplete. If new evidence makes both of our hypotheses less likely, then it's probably smart to check and see if a third hypotheses is now feasible, where it wasn't before.
brazil84 stated that there are just two options, so let's stick to that example first.
"[rifle] no bullet will be find in or around the person's body 0.01% of the time" is contradictory evidence against the rifle (and for the handgun). But "[handgun] no bullet will be find in or around the person's body 0.001% of the time" is even stronger evidence against the handgun (and for the rifle). In total, we have some evidence for the rifle.
Now let's add a .001%-probability that it was not a gunshot wound - in this case, the probability to find...
There are few places where society values rational, objective decision making as much as it values it in judges. While there is a rather cynical discipline called legal realism that says the law is really based on quirks of individual psychology, "what the judge had for breakfast," there's a broad social belief that the decision of judges are unbiased. And where they aren't unbiased, they're biased for Big, Important, Bad reasons, like racism or classism or politics.
It turns out that legal realism is totally wrong. It's not what the judge had for breakfast. It's how recently the judge had breakfast. A a new study (media coverage) on Israeli judges shows that, when making parole decisions, they grant about 65% after meal breaks, and almost all the way down to 0% right before breaks and at the end of the day (i.e. as far from the last break as possible). There's a relatively linear decline between the two points.
Think about this for a moment. A tremendously important decision, determining whether a person will go free or spend years in jail, appears to be substantially determined by an arbitrary factor. Also, note that we don't know if it's the lack of food, the anticipation of a break, or some other factor that is responsible for this. More interestingly, we don't know where the optimal result occurred. It's probably not the near 0% at the end of each work period. But is it the post-break high of 65%? Or were judges being too nice? We know there was bias, but we still don't know when bias occurred.
There are at least two lessons from this. The little, obvious one is to be aware of one's own physical limitations. Avoid making big decisions when tired or hungry - though this doesn't mean you should try to make decisions right after eating. For particularly important decisions, consider contemplating them at different times, if you can. Think about one thing Monday morning, then Wednesday afternoon, then Saturday evening, going only to the point of getting an overall feel for an answer, and not to the point of really making a solid conclusion. Take notes, and then compare them. This may not work perfectly, but it may help you realize inconsistencies, which could help. For big questions, the wisdom of crowds may be helpful - unless it's been a while since most of the crowd had breakfast.
The bigger lesson is one of humility. This provides rather stark evidence that our decisions are not under our control to the extent we believe. We can be influenced by factors we don't even suspect. Even knowing we have been biased, we may still be unable to identify what the correct answer was. While using formal rules and logic may be one of the best approaches to minimizing such errors, even formal rules can fail when applied by biased agents. The biggest, most condemnable biases - like racism - are in some ways less dangerous, because we know we need to look out for them. It's the bias you don't even suspect that can get you. The authors of the study think they basically got lucky with these results - if the effect had been to make decisions arbitrary rather than to increase rejections, this would not have shown up.
When those charged with making impartial decisions that control people's lives are subject to arbitrary forces they never suspected, it shows how important it is and much more we can do to be less wrong.