A theory of contextual propositions for indicative conditionals is presented. The main challenge is to give a precise account of how the dynamics of possible worlds depends on epistemic context. Robert Stalnaker suggested in [Stalnaker 84] that even when selection functions for evaluating indicatives cannot be defined in terms of epistemic context, they can be importantly constrained by a principle of context dependency that we adopt here. In addition, we show how to define a gradation of possibilities for each point in an epistemic context by taking into account a proposal first introduced by Wolfgang Spohn in [Spohn 87] and later refined by Darwiche and Pearl in [Darwiche & Pearl 97]. The resulting theory of contextual propositions (unlike some alternative views) is shown to be compatible with basic qualitative consequences of the Bayesian principle of conditionalization (which is frequently used in probabilistic semantics for indicative conditionals).