An event E has divine-intention probability p if and only if E is part of a system S of events such that there is a probability function P applicable to events in S and God intends S to be such as to be described well by P. For instance, suppose over the history of the world a million coins are tossed and of these 50.1% land heads and other statistical properties of the coin tosses are described well by the assumption that the coin tosses are independent events with each outcome of equal probability. Then if God intended that the coin tosses be such as to be thus described, each coin toss has a divine-intention probability 1/2 of being heads.
In the case of finite sequences, standard frequentism suffers from the problem that it gives intuitively incorrect answers. In the above scenario, it would say that the probability of heads is 0.501. But surely it is possible for a million coins to be tossed, each with probability 1/2 of heads, and yet to get 50.1% of the coins landing heads.
Lewis's regularity theory of laws can get the same result as the theistic version, for in the case of probabilistic laws one trades accuracy against simplicity. But regularity theories of laws get the order of explanation mixed up: chances are supposed to be explanatory rather than descriptive (of course Humeans will say that this is a false dilemma, but they are wrong).