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We define and study logics in the framework of probabilistic team semanticsand over metafinite structures. Our work is paralleled by the recentdevelopment of novel axiomatizable and tractable logics in team semantics thatare closed under the Boolean negation. Our logics employ new probabilisticatoms that resemble so-called extended atoms from the team semanticsliterature. We also define counterparts of our logics over metafinitestructures and show that all of our logics can be translated into functionalfixed point logic implying a polynomial time upper bound for data complexitywith respect to BSS-computations.

On elementary logics for quantitative dependencies