A simple Efimov space with sequentially-nice space of probability measures

Under Jensen's diamond principle ♢, we construct a simple Efimov space K whose space of nonatomic probability measures Pna(K) is first-countable and sequentially compact. These two properties of Pna(K) imply that the space of probability measures P(K) on K is selectively sequentially pseudocompact and the Banach space C(K) of continuous functions on K has the Gelfand-Phillips property. We show also that any sequence of probability measures on K that converges to an atomic measure converges in norm, and any sequence of probability measures on K converging to zero in sup-norm has a subsequence converging to a nonatomic probability measure.