Conditionals have a pervasive role in probability theory. This chapter extends the PSAT \(_\infty \) problem to situations where events are subject to a finite set \(\Theta \) of conditions. Their effect is to restrict the set of “possible worlds” (=  homomorphisms into \({{\,\mathrm{[0,1]}\,}}\) of the ambient MV-algebra of events) to the set of possible worlds where all conditions in \(\Theta \) hold true. Each condition in \(\Theta \) is definable by a formula in Łukasiewicz logic. Extending the results of the foregoing chapter, we will prove the decidability of the resulting “conditional” PSAT \(_\infty \) problem.