Recent experimental research has observed two kinds of priming effects on quantity implicatures. One is the Strong-Weak contrast, where more quantity implicatures are observed after prime trials forcing interpretations with quantity implicatures ('Strong primes') than after prime trials forcing interpretations without quantity implicatures ('Weak primes'). The other effect is the Alternative-Weak contrast, where prime trials mentioning alternative expressions ('Alternative primes') similarly lead to more quantity implicatures. It has been claimed that both of these effects should be understood in terms of increased salience of alternative expressions used to compute quantity implicatures. We present experimental evidence that speaks against this hypothesis. With the help of novel baseline conditions, which were absent in previous studies on implicature priming, we observe that the results in the priming paradigm commonly used in the literature are inverse preference effects in the sense that robust priming effects are observed towards interpretations that are normally unexpected, and depending on the baseline expectation, each of the three prime types mentioned above may have priming effects. We furthermore investigated different types of alternative priming for so-called ad hoc implicatures and found that for these implicatures, presenting an alternative expression in a simple sentence does not have a priming effect on the implicature of a similarly simple sentence, but presenting it in a more complex conjunctive construction does. Our results also show that conjunctions of similar but irrelevant expressions have a similarly robust priming effect and that conjunctive sentences with two conjuncts do not give rise to priming effects on the interpretation of sentences of the same syntactic complexity, but those with three conjuncts do. To make sense of these observations, we propose that what crucially matters for priming implicatures is incremental change in one's probabilistic expectations about the current conversational context brought about by a process we call context adaptation.