you are actually confusing two things (because of notation overloading): the probability of a sequence ASSUMING a model, on one side, and the parameters of a 3-gram model.
Sure we (ab)use the P(..) notation for both of them but strictly speaking they are not the same (although, ASSUMING a given model, some become equal in value).
Maybe another way to answer you is from your claim: we should have P(b|ub) = P(b|bub) :
yes if we are talking about the probability of a sequence assuming a 3-gram,
but NO if we are talking about parameters of a model: the first one is a parameter for a 3-gram model, the second for a 4-gram model. They are NOT the same object (of course, because it's not the same hypotheses).
And, clearly your assessment was wrong : both were provided, the first one being 
, the second 
.
So simply from their values, you already see that these provided 
are not probabilities of sub-sequences, but parameters of different 
-gram model.
I can also explain it differently based on you second claim: no, P(bub) x P(b|bub) x P(l|ubb) x P(e|bl), is NOT a 3-gram parametrization of P(bubble).
I hope I was clear enough. If not, come to me over some break to deepen the question. (the difference between objects computed by a model and the parameters of a model)
