Just now I heard the news, it is so strange that you . . . . . . . not believe it.

The correct answer is: could.

The word “could” is used to express possibility or ability. In this case, the speaker is saying that the news is so strange that it is possible or even likely that the listener would not believe it.

The other options are not as likely because they do not express possibility or ability.

• Will is used to express certainty or prediction. In this case, the speaker is not certain that the listener will not believe the news.
• Might is used to express possibility or uncertainty. In this case, the speaker is not certain that the listener might not believe the news.
• Did is used to express past tense. In this case, the speaker is not talking about the past, but about the present.
• Should is used to express obligation or recommendation. In this case, the speaker is not telling the listener that they should not believe the news.