You’d rather translate croire by "believe" and not "think".

Croire somewhat implies that you trust something and do not question it so je crois qu’il est coupable means "my belief is that he is guilty" and je ne crois pas qu’il est coupable means the opposite, "my belief is that he is not guilty".

Of course, when saying that, you state your opinion and not a fact so are ready to listen to different opinions. A stronger statement would be for example je sais qu’il est coupable with which you do not consider the fact he might be innocent.

With the subjunctive, you still have a belief but about something that involves some uncertainty so the meaning of je ne crois pas qu’il soit coupable tends toward "my belief is that he might not be guilty".

This is particularly hard to explain. Native speakers themselves use the subjunctive without understanding it. But since a distinction still exists, chances are that it serves a purpose in several places.

In your example, if the sentence is meant to provide information or weighs on the process of determining whether Daniel is guilty, indicative will be used. Like any statement it carries doubt and could be subjective. Using the indicative is obviously not a way to get rid of all that.

If the topic of the exchange is something different, the subjunctive is a way to mention whether Daniel is guilty, without weighing on it. In this case you’d rather not assume he is guilty.