A channel can generally be defined by a probability distribution on a set of possible actions. These actions determine the output for any possible input, and are independently drawn. The intrinsic uncertainty of a channel is defined as the conditional entropy of the action given the input and output sequences. For many channels, such as the deletion channel, the insertion channel, and various permutation channels, e.g., the trapdoor channel, quantifying the intrinsic uncertainty is the main challenge in determining the capacity. In this talk, we derive an alternative expression for the intrinsic uncertainty via the Laplace variational principle, and utilize it to obtain a general lower bound on the capacity, which is then applied in several examples.