The form for the Subjunctive and Doubt & Denial is the required 3-part formula.
When expressing doubt, the focus isn't on the veracity or reality of any facts but rather on your personal lack of belief in them. For example:
|I doubt the Steelers are going to win the Superbowl again!||Yo dudo que los Steeler gane el Superbowl otra vez [Subjunctive]|
But maybe my dad disagrees. He believes they WILL win:
|I think they are going to win it!||¡Creo que van a ganarlo! [Indicative]|
Whether or not the Steelers actually win is irrelevant at this moment. It is our belief (or lack thereof) in whether or not they win that determines the use of the Subjunctive.
In the first example my doubt indicates I am describing a scenario I find unreal. Therefore, I need to use the Subjunctive to express that doubt.
In the second example, my father is describing what he believes is reality and therefore he uses the indicative present tense -NOT the Subjunctive- to express it.
Let's look at another example:
|I deny that UFOs exist||"Niego que existan los OVNIs" [Subjunctive]|
But Scully and Mulder disagree:
|"We do not doubt that UFOs exist!"||"No negamos que existen los OVNIs" [Indicative].|
They "do not doubt" which means they "are sure or believe" that UFOs exist. So they use the Present tense indicative to express this belief.
With Spanish, when belief is 100%, the Present tense indicative is used. If there is a shred of doubt - even if something is probable there is still doubt - , then the Subjunctive must be used.