@ John It's "ambiguity", not "ambigity".

The textbook is right, a is more appropriate. All the context necessary is given in the screenshot, the person who said the sentence is a newsreader. The difference is subtle. The newsreader is reporting something that will definitely happen in the future. It is a statement of fact. It will happen, no ifs, no buts, no maybes. Do you see the difference? If you use 'going to', although we understand as a listener it is highly likely that the said event is going to happen, it leaves open the possibility (however small it might be) that it is open to change. The King should arrive at 6, that is what is scheduled to happen. That is what we understand. But A leaves no leeway, no wiggle room which B does. For that reason B sounds weird in the context provided.

Be going to is used 1- predition based on present evidence. E.g. look at that wall, it looks as if it is going to fall down 2- intentions E.g. I am asking for a pay rise tomorrow. While will used as 1- prediciton 2- future fact 3- Decisions made at the moment of speaking 4- offers 5- promises 6- requests 7- refusal (won't) a is correct becuse it gives future fact

You might find this chart on the differences between WILL and GOING TO helpful: http://www.grammar.cl/Notes/Future_Will_vs_Going.htm

The correct answer is "both are the same" researched and verified on behalf of the asker. There are no subtle differences or nuances. The asker has been messaged with a simple explanation, as per my comment above. The only exception is "Will grammar" is much more common in official timetables. Therefore Dan N should be selected as the best answer.