This paper gives an explication of our intuitive notion of strength of justification in a controversial debate. It defines a thesis' degree of justification within the bipolar argumentation framework of the theory of dialectical structures as the ratio of coherently adoptable positions according to which that thesis is true over all coherently adoptable positions. Broadening this definition, the notion of conditional degree of justification, i.e.\ degree of partial entailment, is introduced. Thus defined degrees of justification correspond to our pre-theoretic intuitions (...) in the sense that supporting and defending a thesis t increases, whereas attacking it decreases, t's degree of justification. Moreover, it is shown that (conditional) degrees of justification are (conditional) probabilities. Eventually, the paper explains that it is rational to believe theses with a high degree of justification insofar as this strengthens the robustness of one's position. (shrink)