Defining deterministic causation is tough. Standard definitions of "causal determinism" do not do justice to the causal aspect of the determinism. The natural suggestion that A deterministically causes B provided that the occurrence of A conjoined with the laws of nature entails B doesn't work if the laws are ceteris paribus (I'm grateful to Jon Kvanvig for this point) and is in any case subject to counterexample.
I don't have a definition here. But I do have a way to point to the notion, by way of analogy. Start with the notion of probabilistic causation of strength s, where s is a number between 0 and 1. If C probabilistically causes E with strength s, then C has a disposition of strength s to produce E. Moreover, normally—but this can be finked—the probability of E given C and the laws will be s, and tis probability will be explained by the probabilistic tendency of strength s of C to produce E.
Deterministic causation then is a kind of limiting case of probabilistic causation. C's deterministically causing E is a relation that stands to the condition that, if everything is normal, the occurrence of C and the laws entail E in the way in which C's probabilistically causing C with strength s stands to the condition that, if everything is normal, the occurrence of C and laws give probability s to E.
This gives us an account of deterministic causation by analogy.
The tempting suggestion that deterministic causation is just the s=1 special case of probabilistic causation is insufficient, since events of zero probability can happen. However, it is correct to say that deterministic causation is a special case of probabilistic causation of strength 1.