How is the question of the colour of your shirt of any relevance to the question of belief of "eating W"?

It's not relevant.

To your question the answer is "I don't know", while the answer to do you believe I ate or do you believe I didn't eat has a definite answer; while to your question there are more than two options, it's not binary, either 0 or 1.

There's no room for comparison between the two questions.

How is the question of the colour of your shirt of any relevance to the question of belief of "eating W"? — MathematicalPhysicist

The question can be rephrased as "for any given colour, do you believe it is that colour or not?".

To your question the answer is "I don't know", while the answer to do you believe I ate or do you believe I didn't eat has a definite answer; while to your question there are more than two options, it's not binary, either 0 or 1. — MathematicalPhysicist

Whether the options are binary is not relevant, you believe that one must believe in some value.

I don't believe the present king of France is bald.
<ducks>

Funny enough, there are currently 3 different aspirants to the throne of France. And one of them is bald.

If only I could upvote you! Thank you, my friend.

the answer to do you believe I ate or do you believe I didn't eat has a definite answer — MathematicalPhysicist

It has no answer because it is a false dichotomy. The question presupposes that one either believes W or one believes ~W. It erroneously omits the possibility that one could believe neither. It also omits the somewhat more controversial possibility that one could believe both. One can debate whether that last is possible. But it nevertheless needs to be included in the quartet, to complete the analysis.

For the vast majority of well-formed propositions that can be made, I believe neither the proposition nor its negation, because I am in no position to form an opinion either way.

It would be very sad if we were to ban the state of suspended judgement. It seems to me that that is one of the most beautiful states there is.