Suppose there is an infinite line of paving stones, labeled 1, 2, 3, ..., on each of which there is a blindfolded person. You are one of these persons. That's all you know. How likely is it you're on a number not divisible by ten? The obvious answer is: 9/10. But now I give you a bit more information. Yesterday, all the same people were standing on the paving stones, but differently arranged. At midnight, all the people were teleported, in such a way that the people who yesterday were standing on numbers divisible by ten are now standing on numbers not divisible by ten, and vice versa. Should you change your estimate of the likelihood you're on a number divisible by ten?
Suppose you stick to your current estimate. Then we can ask: How likely is it that you were yesterday on a number not divisible by ten? Exactly the same reasoning that led to your 9/10 answer now should give you a 9/10 answer to the back-dated question. But the two probabilities are inconsistent: you've assigned probability 9/10 to the proposition p1 that yesterday you were on a number not divisible by ten and 9/10 to the proposition p2 that today you are on a number not divisible by ten, even though p1 holds if and only if p2 does not (this violates finite additivity).
So you better not stick to your current estimate. You have two natural choices left. Switch to 1/2 or switch to 1/10. Switching to 1/2 is not reasonable. Let's imagine that today is the earlier day, and you have a button you can choose to press. If you press it, the big switch will happen—the folks on numbers divisible by ten will be swapped with the folks on numbers not divisible by ten. If you had switched to 1/2 in my earlier story, then if you press the button, you should also switch your probabilities to 1/2, while if you don't press the button, you should clearly stick with 9/10. But it's absurd that your decision whether to press the button or not should affect your probabilities (assume that there is no correlation between what decision you make and what number you're on).
Alright, so the right answer seems to be: switch to 1/10. But this means that the governing probabilities in infinite cases are those derived from the initial arrangements. Why should that be so?
Here is a suggestion. We assume that the initial arrangement came from some sort of a regular process, perhaps stochastic (where "regular" is understood in the same sense as "regularity" in discussions of laws). For instance, maybe God or a natural process brought about which squares the people go on by taking the people one by one, and assigning them to squares using some natural probability distribution, like probability 1/2 to 1, 1/4 to 2, 1/8 to 3, and so on, with the assignment being iterated until a vacant square is found (equivalently do it in one step: use this distribution but condition on vacancy). And, maybe, for most of the "regular" distributions, once enough people are laid down, we get about a 9/10 chance that the process will land you on a square not divisible by ten.
This assumes, however, that there is a process that puts people on squares. Suppose this assumption is false. Then there seems to be no reason to privilege the probability distribution from the first time the folks are put on squares. And our intuitions now lead to inconsistency: assigning 9/10 to p1 and 9/10 to p2.
Where has all this got us? I think there is an argument here that absurdity results from an actual, simultaneous infinity of uncaused objects. But if an actual infinity of objects is possible, and it is possible to have a contingent uncaused object, then it is very plausible (this is an ampliative inference) that it is possible to have an actual infinity of simultaneous contingent uncaused objects.
Therefore: either it is impossible to have an uncaused object or it is impossible to have an actual infinity of simultaneous contingent objects. But it is possible to have an actual infinity of simultaneous contingent objects if it is possible to have an infinite past. This follows by al-Ghazali's argument: just imagine at each past day a new immortal soul coming into existence, and observe that by now we'll have a simultaneous infinity of objects. So, it is either impossible to have an uncaused contingent object or it is impossible to have an infinite past. We thus have an argument for the disjunction of the premises of the Kalaam argument, which is kind of cool, since both of the premises of the argument have been disputed. Of course, it would be nicer to have an argument for their conjunction. But this is some progress. And it may be the further thought along these lines will yield more fruit.