  We present a construction for the composition of subsequential transducers
(representing conditional probabilistic models) with subsequential failure
transducers (representing probabilistic models). Under certain conditions,
satisfied by the corresponding transduction devices, a more efficient
construction is applicable that avoids the creation of unnecessary states.
Furthermore, the weights of the resulting failure transducers can be
efficiently redistributed via weight pushing in the $\langle \mathbb{R}_+, +,
\times, 0, 1 \rangle$ and $\langle \mathbb{R}_+, \max, \times, 0, 1 \rangle$
semirings.
