By means of Borel probability measures on the valuation set endowed with the usual product topology, the notion of probability truth degrees of propositions in n-valued and [0,1]-valued Łukasiewicz propositional logics is introduced. Its basic properties are investigated, and the integral representation theorem and the limit theorem of probability truth degree functions in n-valued case, in particular, are obtained. Theses results show that the notion of truth degree existing in quantitative logic is just a particular case of Borel probability truth degrees, and a more general quantitative model based on the notion of Borel probability truth degree for uncertainty reasoning can be then established.