Two strong contenders for scalar implicature (SI) computation are the pragmatic and the grammatical theories. While the former sustains that context plays a major role, the latter suggests context is required but is lexically and monotonically constrained (Chierchia 2012). In particular, this paper discusses a processing account for SIs that is dependent on the satisfaction of the Strawsonian presupposition of existence, necessary for the realization of the asymmetric entailment pattern among relevant alternatives. This observation complies with the principles of the grammatical view, for it predicts SIs in the presence of contextually empty domains, unlike the pragmatic account whose necessary access to contextual information will cause propositions with empty domains to always return a truth value false, hence blocking any inference.  I present online experimental evidence of an acceptability judgment task and recorded response times of both existential and universal sentences containing entities of three kinds: existent (type-a), non-existent but conceivable (type-b), and non-existent and inconceivable (type-c). The data of 25 Colombian Spanish speaking participants were collected using PsychoPy, powered by Pavlovia. The results suggest SIs are computed in types a and b but relatively unsuccessful in type-c. I conclude that the relevant entailment pattern for implicature computation is the Strawson-entailment relation which, combined with the grammatical account, correctly predicts SIs with non-existent but conceivable entities but avoids inference with inconceivable terms.