'Shall' isn't right! For neutral statements and predictions about the future, 'shall' is the modal for the first person ( I shall/we shall) - the modal for 'you' is 'will'. We only use 'shall' with the second person (you) for special emphasis: for example, to contradict a previous statement, to issue a command, grant permission and so on. For a prediction - in essence, a situation over which the speaker has no control - the correct form is 'I predict that you will ....' (NOT shall). I wonder if the answer is meant to be (a) and the lack of 'to' is simply a typo. Then someone, at a later point, got hold of the version with this typo and assumed that the answer must be 'shall'.

Sheena is right in that the question is not a very good one. However we are dealing with what 'is' there and not what 'would be' correct. The only answer which fits is 'shall' is the only one which will give a gramatically correct answer. As my old primary school headmaster used to say to whoever came top in the class "The best of a VERY BAD bunch"

Well, in traditional British grammar, the rule is that will should only be used with second and third person pronouns (you; he, she, it, they). With first person pronouns (I and we), the 'correct' verb to talk about the future is shall. This link might help you understand https://www.google.com/imgres?imgurl=http://media.llb.re.s3.amazonaws.com/pub/notes/will_would.jpg&imgrefurl=http://languagelearningbase.com/88531/when-to-use-will-shall-would-and-should-will-have-or-would-have&h=1200&w=1040&tbnid=tXWCtaKCibEd8M:&q=When+to+use+shall+and+will&tbnh=160&tbnw=138&usg=AI4_-kSPX_pc5rDA1Q2GM-teVAt-V991EA&vet=12ahUKEwiA6Yi-1_XfAhVsHzQIHT8ADysQ9QEwAHoECAgQBg..i&docid=zQLx1DM_aN9mNM&sa=X&ved=2ahUKEwiA6Yi-1_XfAhVsHzQIHT8ADysQ9QEwAHoECAgQBg

Hi, Sasha. "I predict that you SHALL marry someone rich and famous" is VERY old-fashioned, and not really correct in this context. "I predict that you ARE GOING TO marry someone rich and famous" is fine, but you need the 'TO' (are going to, not 'are going'). "I predict that you WILL marry someone rich and famous" is also fine, and probably the best option. For predictions where we have no evidence, 'will' is best. (I think he'll fail) (I imagine she'll get top marks) etc. For predictions based on evidence, 'going to' is better. (There are dark clouds out there. I think it's going to rain.) (That tree is leaning sideways. It's going to fall!) I don't know where you found the exercise with only those three options, but I would question whether the person who wrote it knows English very well. I hope that was helpful.

To put it really simple, it's because you're talking about a probability. 'You' are not sure whether he/she is going to marry, you predict it!