This decomposition of P(T | S) is useful in two ways: first, it makes it possible to ignore P(S) when searching forT; second, it allows us to concentrate our efforts on the lexical aspects of P(S | T), leaving it to P(T) (the "target language model") to take care of syntactic and other language-specific aspects.
in one of the simplest and earliest statistical translation models, iBM's Model 1, it is assumed that P(S | T) can be approximated by a computation that uses only "lexical" probabilities P(s | t) over source and target language words s and t. this model completely disregards the order in which the individual words of S and T appear.