That's a very good question. I would describe it this way: To speak of something happening by chance, we are saying that it does not require the action of a direct, intelligent agent, nor does it require a particular configuration of operational constraints (natural laws and immediate environmental causes), such that a given outcome becomes inevitable, given probabilistic resources for any chance elements within the scenario in question.
OK, that's a mouthful. Let me try to provide an illustration that is probably more helpful:
We enter a room and notice a variety of marbles of different colors sitting on the floor in an apparently random pattern. We are asked to consider whether the position of the marbles is due to (1) chance, (2) order, or (3) an intelligent agent.
The first thing we notice is the random scattering of all the marbles. There is no need to appeal to anything more than chance in the scattering of these marbles. But then we reflect a moment, and realize the marbles could be randomly scattered at all heights in the room, floating in mid-air. Why aren't they?
The answer, of course, is the law of gravity. Gravity is causing a layer of order in the results, the random scattering on the floor not-withstanding. So there is a mixture of chance and order that needs to be invoked in the overall explanation here.
And then, if we notice that the red marbles alone, of all the colors, spell out a word in English, we would have evidence for a cause not explainable by chance nor by natural laws/order.
I'm not sure I've answered the question, or gone down a rabbit trail. I apologize if the latter...
Doesn't biochemistry and other natural processes such as snowflake formation work the same way, a combination of natural law, and chance?
And then, if we notice that the red marbles alone, of all the colors, spell out a word in English, we would have evidence for a cause not explainable by chance nor by natural laws/order.
What if the marbles are dropped a billion times, and one of those drops out of a billion yields a word in English spelled by the red marbles?
There are difficult computational problems that aren't solvable (or easily solved) by algorithms alone, but are solvable when the algorithms are combined with chance or randomness. Perhaps God is a better problem solver than some people think.
I'm not sure I've answered the question, or gone down a rabbit trail. I apologize if the latter...
Good answer. Good post.