This paper investigates the dynamic consistent updates of incomplete preferences relations in the class of variational Bewley preferences (VBP). We show that this conditional preferences are also VBP that reveals the same ranking over consequences as the unconditional relation and are represented by an ambiguity index obtained through the full Bayesian update of the ex ante ambiguity index. Moreover, we study ex post forced choice relations, which captures choices that must be taken by a decision maker after learning some relevant event. Formally, they are monotone continuous weak orders. We show that any ex post forced choice relation that preserves the ambiguity attitudes of a given ex ante VBP has a variational functional representation with the same raking over consequences and the ambiguity index of the corresponding dynamic consistent update. Thus, our result can be viewed as a novel foundation for the full Bayesian update for the class of variational preferences.