simon,
Actually, I think it might (though I'm obviously open to correction) if you take the anthropic principle as a given (which I do not).
One thing you're missing is that there are two events here, call them A and B:
A. LHC would destroy earth B. LHC works
So the events, which are NOT independent, should look more like:
Outcome 2 is "closer" to outcome 1. More precisely, evidence that 2 occured would increase our probability of both A and B, which would therefore decrease the probability of event 3 relative to event 1.
The fact that 2 is invisible means that we can't tell when it has happened. But there is a chance that it is happening that would increase with each subsequent failure, as Eliezer noted.
This is far from formal but I hope I'm getting the gist across.
Recently the Large Hadron Collider was damaged by a mechanical failure. This requires the collider to be warmed up, repaired, and then cooled down again, so we're looking at a two-month delay.
Inevitably, many commenters said, "Anthropic principle! If the LHC had worked, it would have produced a black hole or strangelet or vacuum failure, and we wouldn't be here!"
This remark may be somewhat premature, since I don't think we're yet at the point in time when the LHC would have started producing collisions if not for this malfunction. However, a few weeks(?) from now, the "Anthropic!" hypothesis will start to make sense, assuming it can make sense at all. (Does this mean we can foresee executing a future probability update, but can't go ahead and update now?)
As you know, I don't spend much time worrying about the Large Hadron Collider when I've got much larger existential-risk-fish to fry. However, there's an exercise in probability theory (which I first picked up from E.T. Jaynes) along the lines of, "How many times does a coin have to come up heads before you believe the coin is fixed?" This tells you how low your prior probability is for the hypothesis. If a coin comes up heads only twice, that's definitely not a good reason to believe it's fixed, unless you already suspected from the beginning. But if it comes up heads 100 times, it's taking you too long to notice.
So - taking into account the previous cancellation of the Superconducting Supercollider (SSC) - how many times does the LHC have to fail before you'll start considering an anthropic explanation? 10? 20? 50?
After observing empirically that the LHC had failed 100 times in a row, would you endorse a policy of keeping the LHC powered up, but trying to fire it again only in the event of, say, nuclear terrorism or a global economic crash?