In literature, different deductive systems are developed for probability logics.   But, for formulas,  they provide esstentially equivalent definitions of consistency.   In this talk, we present a guided maximally consistent extension theorem which says that any probability assignment to formulas in a finite local language satisfying some constraints specified by probability formulas is consistent in probability logics.  Moreover, we employ this theorem to show two interesting results:
 
(1) The satisfiability of a probability formula is equivalent to the solvability of the corresponding system of linear inequalities through a certain translation based on atoms not on Hintikka sets;
 
(2)  the Countably Additivity Rule In Goldblatt 2009 is necessary for his deductive construction of final coalgebras for functors over Meas.