Since P(S) = P(S|A)P(A) + P(S|-A)P(-A), and P(S|A)P(A) is already .99, then P(S) cannot be .000001. Those two assertions are contradicting each other: you cannot coherently believe a composite event (suriving an illness) less than you believe each factor (surviving the illness with the aid of magic).
If you believe that God will cure everyone who gets the disease (P(S|A) = 1) and God is already a certainty (P(A) = .99), then why so few people survive the illness?
One possibility is that it’s P(S|-A) that is one in a million (surviving without God is extremely rare). In this case:
If you already believe that curing aliens are a certainty, then for sure surviving an illness that has only a millionth possibility otherwise, will bring up your belief up to almost a certainty.
Another possible interpretation, that keeps P(S) = .000001, is that P(S|A) is not the certainty. Possibly God will not cure everyone who gets the disease, but only those who deserves it, and this explains why so few survive.
In this case:
P(S) = x .99 + y .01 = .000001 --> P(A|S) = x * .99 / .000001
a number that depends on how many people God considers worthy of surviving.
This.
Since P(S) = P(S|A)P(A) + P(S|-A)P(-A), and P(S|A)P(A) is already .99, then P(S) cannot be .000001.
Those two assertions are contradicting each other: you cannot coherently believe a composite event (suriving an illness) less than you believe each factor (surviving the illness with the aid of magic).
If you believe that God will cure everyone who gets the disease (P(S|A) = 1) and God is already a certainty (P(A) = .99), then why so few people survive the illness?
One possibility is that it’s P(S|-A) that is one in a million (surviving without God is extremely rare). In this case:
P(A|S) = P(S|A) P(A) / P(S) -->
P(A|S) = P(S|A) P(A) / (P(S|A) P(A) + P(S|-A) P(-A)) -->
P(A|S) =1 .99 / (1 .99 + .000001 * .01) -->
P(A|S) = .99 / (.99 + .00000001) -->
P(A|S) = .99 / .99000001 -->
P(A|S) = .9999999...
If you already believe that curing aliens are a certainty, then for sure surviving an illness that has only a millionth possibility otherwise, will bring up your belief up to almost a certainty.
Another possible interpretation, that keeps P(S) = .000001, is that P(S|A) is not the certainty. Possibly God will not cure everyone who gets the disease, but only those who deserves it, and this explains why so few survive.
In this case:
P(S) = x .99 + y .01 = .000001 -->
P(A|S) = x * .99 / .000001
a number that depends on how many people God considers worthy of surviving.