  We introduce Probabilistic Guarded Kleene Algebra with Tests (ProbGKAT), an
extension of GKAT that allows reasoning about uninterpreted imperative programs
with probabilistic branching. We give its operational semantics in terms of
special class of probabilistic automata. We give a sound and complete
Salomaa-style axiomatisation of bisimilarity of ProbGKAT expressions. Finally,
we show that bisimilarity of ProbGKAT expressions can be decided in $O(n^3 \log
n)$ time via a generic partition refinement algorithm.
