Causal decision theory \(the current standard\) says we should instead use the counterfactual conditional $~$\\ \\mathbb P(a\_x \\ \\square \\! \\! \\rightarrow o\_i).$~$

The expression P(a*x [ ]-> o*i) is meaningless. Probability theory is an extension of classical propositional logic (CPL) to express degrees of certainty; probabilities are assigned to CPL formulas. "a*x [ ]-> o*i" is not a CPL formula, as there is no counterfactual conditional operator in CPL.