Clarifying the Probabilistic Argument from Evil
Properly understood, the inductive (or probabilistic, as it is sometimes called) argument from evil is itself presenting a logical problem of evil, insofar as the fundamental claim remains between the strict incompatibility between God and unjustified evils.
The question is whether the move from “I do not see a reason for this instance of evil,” to “Probably, there is no reason,” is 1) legitimate, and 2), if so, then whatever strength one affords to the “probably” in that sentence, is the degree to which they should think that God does not exist.
Obviously, if we knew there were unjustified evils, we would know that God does not exist. The probabilistic argument from evil is about assigning some significant credence to the idea that there actually are unjustified evils. In other words, it is not that there definitely are unjustified evils and because of that God probably does not exist. That is absurd: If there definitely are unjustified evils then God definitely does not exist. Rather, the argument is: Probably there are unjustified evils, and for that we reason we should lean toward atheism.
Contrarily, a committed theist might counter with a Moorean Shift: affirming God's existence (based on certain reasons) and thus denying the existence of unjustified evils, even without understanding the justifying reasons.
That’s all very quick, of course. For more, I respond to various problems of evil at length in my book The Best Argument for God.
https://www.amazon.com/Best-Argument-God-Patrick-Flynn/dp/1644137801/ref=mp_s_a_1_1?crid=32ICSENVQ6085&keywords=the+best+argument+for+god+patrick+flynn&qid=1700587556&sprefix=the+best+argumen%2Caps%2C202&sr=8-1