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This paper introduces a framework for building probabilistic models with subsequential failure transducers. We first show how various types of subsequential transducers commonly used in natural language processing are represented by conditional probabilistic subsequential transducers and probabilistic subsequential failure transducers. Afterwards, we introduce efficient algorithms for composition of conditional probabilistic subsequential transducers with probabilistic subsequential failure transducers and canonization (weight-pushing) of probabilistic subsequential failure transducers. Those algorithms are applicable to many tasks for representing probabilistic models. One such task is the construction of the [Formula: see text] weighted transducer used in speech recognition which we describe in detail. At the end, a comparison between the presented [Formula: see text] failure weighted transducer and the standard [Formula: see text] weighted transducer along with empirical results for HMM-based speech recognition decoding reveal the competitiveness of the presented constructions.