First, note that every word has a semantic range (different senses in which the word is understood). When a word is used often, its semantic range tends to be correspondingly broad.
“Must” and “will” are both common words, and their semantic ranges are both quite broad. Hence even though the semantic ranges overlap, it can be difficult to pin down exactly when that occurs. A lot of idiomacy depends on usage, and usage doesn’t always follow simple rules of logic.
In the context of “inferred probability”, you can use a rule of thumb that “must” often carries a sense that there is an implied alternative that is considered to be unlikely but possible.
- Someone’s knocking on the door. That must be the neighbour.
The implied alternative is that someone or something else could have knocked on the door. Perhaps it’s the police, or an uncle, or even just a pebble blown ‘just right’ by a gust of air. However, your neighbour borrowed your lawn mower and said he’d return it at about this time, so all those alternatives are unlikely.
This rule of thumb is complicated by various factors, including the use of sarcasm.
The corresponding rule of thumb for “will” in this context is that it is a prediction. Although the prediction could turn out to be wrong, there is usually no alternative hypothesis that is being implied.
- Someone’s knocking on the door. That will be the neighbour.
Here, if it turned out to be the police, the speaker was merely wrong; using “will” doesn’t convey the notion that any alternative was even hinted at or open to consideration.
Again, note that the semantic ranges of will and must are very broad. The above is merely a rule of thumb for choosing between the two in a specific context. There can be cases where the rule of thumb fails, in which case the context will need to inform the choice of which to use.
In comments, you indicated that you are particularly interested in why pairs like the following aren't equivalent:
- You will be French; and
- You must be French.
The reason is that although each word has a semantic range, each context can fit one part of the range much better than another.
Here, "will" comes out more strongly as either a command or a statement about the future, and a lot less strongly as a statement (whether with or without implied alternatives) about the present. Your referenced book notes this by saying, "particularly about the immediate future" - the word future is significant.
You can get closer to the "must" version if you shift the sentence into the past: "You would be French [, then]." Adding the word "then" emphasises that the statement is a conclusion or observation rather than a prediction or command. Adding it to the original has a similar effect: "You will be French, then", though the strong 'future' sense of will still bleeds through and makes the statement more awkward than "You must be French, then".
You might ask why, then, "That'll be the 5:15 train" works as well as "That must be the 5:15 train". The answer is that if you look a little deeper, they communicate something slightly different, but the overall effect is similar.
The "will" version makes a prediction (or a guess) about the identity or some property of "that". The "must" version makes a statement about the same thing. However, since the identity/property carries the most weight either way, it is inconsequential whether the information is conveyed as a prediction/guess or a statement.
