An uncertain variable, U, is conditionally independent of variables V₁, ..., V_n given variables W₁, ..., W_m, if its conditional probability distribution is identical whether or not it explicitly accounts for V₁, ..., V_n. Mathematically, conditional independence implies that {U | W₁, ..., W_m, E} = {U | W₁, ..., W_m, V₁, ..., V_n, E}, where E represents the background state of information under which the distribution is assessed. In a relevance diagram, conditional independence is denoted by the absence of arrows between nodes that are conditionally independent given their direct predecessors. In practice, most assertions of independence result from an underlying understanding of the behavior of the variables being represented.

See also: Dependence, Expert, Mutual Independence, Outcome, Pairwise Independence and Pedigree.