This article proposes a systematic study of information flow in credential-based declarative authorization policies. It argues that a treatment in terms of information flow is needed to adequately describe, analyze and mitigate a class of probing attacks which allow an adversary to infer any confidential fact within a policy. Two information flow properties that have been studied in the context of state transition systems, non-interference and opacity, are reformulated in the current context of policy languages. A comparison between these properties reveals that opacity is the more useful, and more general of the two; indeed, it is shown that non-interference can be stated in terms of opacity. The article then presents an inference system for non-opacity, or detectability, in Datalog-based policies. Finally, a pragmatic method is presented, based on a mild modification of the mechanics of delegation, for preventing a particularly dangerous kind of probing attack that abuses delegation of authority.