(Explanations on the basis of A Comprehensive Grammar of the English Language, Quirk et al, 1985)
It can stand alone according to the two modalities (volition as insistence, mood marker) that are indicated by the contexts.
I
Example
- He had tried to make up with her, telling her that whatever wrong he had done to her was in reality not of his own doing, that he was a victim of circumstances, and that he was only now in a position to explain to her. She would never believe his story.
In this paragraph, "would" is the modal in its function of expressing volition. Out of 3 possible sorts of volitional attitudes (intention, willingness, insistence: "He said he would phone after lunch", "Would you help?", "She would keep interrupting me."), the relevant variant here to be contended with is insistence.
II
If I use "She would never believe his story." independently, does it mean that I am not sure that she would never believe his story? If I am not sure, isn't it better that I say, "She would probably not believe his story".?
No, on the contrary, you mean that you are sure that she never will believe it, if someone told her. However, if you are not quite sure, then the addition of "probably" makes that clear. You are not now considering the use of this modal according to the scheme examined above. The function of modal "would" is now that of marker of hypothetical meaning. It can be used independently according to the fact that there is an implicit if-subordinate that results from the context.
Example
- — So you are saying that he intends to tell her that he did not have enough time during the weekends? She knows he has been playing volleyball for hours every weekend during the summer; she would never believe his story.