Koopman [14–16] introduces such a quaternary relation \(\succsim \) that \((A,B)\succsim (C,D)\) is interpreted to mean that A given B is at least as probable as C given D. Recently Mundici [24] and Ibeling et al. [13] respectively have investigated Koopman’s qualitative conditional probability from a logical point of view. However, the complete axiomatization of logic of qualitative conditional probability has been an open problem. The aim of this paper is to propose a new version of complete logic–Logic of Qualitative Conditional Probability ( \(\textsf{LQCP}\) ) by proving a theorem that can bridge the gap between the semantics and the axiomatization of \(\textsf{LQCP}\) .