A key factor in the derivation of an optional inference from a certain utterance is how likely the inference is given the context, as modified by the utterance itself. We argue that this factor can account for the inference patterns of sentences with multiple scalar items. Moreover, it alleviates the need of and makes better prediction than a hard constraint on multiple replacements, which has been proposed in connection with those patterns (Fox 2007, Magri 2009). How this idea relates to recent proposals, trying to reduce scalar implicatures altogether to probabilistic reasoning remains to be investigated (e.g., Russell 2012, Potts, Lassiter, Levy & Frank 2015), but we propose that likelihood considerations ought to play a role in all approaches, in determining how to interpret an ambiguous message. Finally, we outline two possible extensions of the proposal to other domains. The first has to do with how information may be packaged. In particular, the idea is that it is pragmatically odd to convey one’s key message through an inference rather than through assertive components. Hence, it would be infelicitous or marked to use a sentence S if S is highly probable (low information) but S enriched with its inference is much less probable (high information). Relatedly, in a different domain, an unlikely presupposition may resist accommodation, especially if the assertive component is itself unsurprising. The second extension has to do with the so-called symmetry problem for theories of alternatives (Katzir 2007, Fox & Katzir 2011). We speculate that the difference in likelihood between symmetric alternatives could provide a principled way of choosing between them.