Causal Explanations Need Not Increase the Probability of Events

I recently came across this argument, which purports to refute the argument from contingency:

1. Suppose that some necessary proposition q causally explains a contingent proposition p.
2. A proposition q only causally explains a proposition p if q is true.
3. So, q is a necessary truth. (From 1 and 2)
4. The probability of a necessary truth is 1.
5. So, P(q) is equal to 1. (From 3 and 4)
6. Then, P(p|q) is equal to P(p). (From 2 and 5)
7. But, if q causally explains p, then P(p|q) > P(p).
8.  So, q does not causally explain p.
9. Then, q both does and does not causally explain p, which is absurd. (From 1 and 8)
10. Therefore, no necessary proposition causally explains a contingent proposition.

The essential premise here is (7), which the author summarizes thusly: "though causal explanations may neither entail nor make probable what they explain, it is at least true of causal explanations that their being true increases the probability of that which they explain." 

However, on closer examination, we see that this is flatly false. For it is well-known in philosophy of science that an explanation can reduce the probability of an event that it explains (thanks to Alexander Pruss for the following example). Suppose that Todd is a skilled assassin, who has been hired to kill Carl. When Todd fires his gun, there is a 99% chance that his target will die. As he is lining up his shot, Bob, a less effective assassin, also shows up. When Bob fires his gun, there is a 60% chance that his target will die. Bob, who compensates for his lack of precision with speed, gets his shot off first, and Todd flees the scene, never firing his gun. As it happens, Bob's shot kills Carl (though if he had missed, due to Todd's flight, Carl would have lived).

Here we have a case of a clear causal explanation, which nevertheless reduces the probability of the event that it explains. Bob's gunshot provides a causal explanation of Carl's death, despite the fact that it reduced Carl's chance of dying from 99% down to 60%. In other words, P(Carl's death | Bob's shot) is 60%, while P(Carl's death) without Bob's shot is 99%. So, by premise (7), we should say that Bob did not cause Carl's death, which is absurd.

At the end of the aforementioned "refutation," the author attempts to rebut these sorts of examples. He claims that, while the less effective assassin may reduce the target's chance of death relative to the more effective assassin, they nevertheless increase the probability simpliciter. I would argue that his objections fail; by premise (7), the probability of p occurring without q must be lower than it is with q in order for q to count as a causal explanation. Therefore, if the probability of p would be higher in the absence of q, premise (7) would tell us that q cannot be a causal explanation of p. This would require us to embrace the absurd conclusion that Bob did not cause Carl's death. The author of this supposed "refutation" should either revise premise (7), or acknowledge that his argument is a failure.

Just for the sake of argument, there are other examples we can give to illustrate this general issue. Suppose that there were an infinite series of snipers lined up to kill Carl, all firing one after another, and all with a non-zero chance of hitting their target. Here Carl's chance of death is 100%, and no individual sniper can affect this probability in any way (since even if he were to pack up his rifle and go home, there would be an infinite number of substitutes). But of course, one of the snipers must inevitably be the one to fire the fatal shot. From this, we can generate a problem for our interlocutor.

Suppose snipers one through thirty miss their target, and sniper thirty-one makes the kill. If he had missed, there would have been an infinite number of snipers after him, one of whom would have hit the mark; that is, the probability of Carl's death is 100%, whether sniper thirty-one is there or not. Therefore, P(Carl's death | Sniper Thirty-One) = P(Carl's death). But then, by premise (7) we should deny that sniper thirty-one caused Carl's death, which is absurd.

The conclusion, therefore, is that causal explanations need not increase the probability of the events that they explain. Thus, the supposed refutation of the argument from contingency fails.