Bayesian networks (BN) are probabilistic graphical models that enable efficient knowledge representation and inference. These have proven effective across diverse domains, including healthcare, bioinformatics and economics. The structure and parameters of a BN can be obtained by domain experts or directly learned from available data. However, as privacy concerns escalate, it becomes increasingly critical for publicly released models to safeguard sensitive information in training data. Typically, released models do not prioritize privacy by design. In particular, tracing attacks from adversaries can combine the released BN with auxiliary data to determine whether specific individuals belong to the data from which the BN was learned. State-of-the-art protection tecniques involve introducing noise into the learned parameters. While this offers robust protection against tracing attacks, it significantly impacts the model's utility, in terms of both the significance and accuracy of the resulting inferences. Hence, high privacy may be attained at the cost of releasing a possibly ineffective model. This paper introduces credal networks (CN) as a novel solution for balancing the model's privacy and utility. After adapting the notion of tracing attacks, we demonstrate that a CN enables the masking of the learned BN, thereby reducing the probability of successful attacks. As CNs are obfuscated but not noisy versions of BNs, they can achieve meaningful inferences while safeguarding privacy. Moreover, we identify key learning information that must be concealed to prevent attackers from recovering the underlying BN. Finally, we conduct a set of numerical experiments to analyze how privacy gains can be modulated by tuning the CN hyperparameters. Our results confirm that CNs provide a principled, practical, and effective approach towards the development of privacy-aware probabilistic graphical models.