∀ {α : Type u_1} {β : Type u_2} {Ω : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  {mΩ : MeasurableSpace Ω} [inst : Countable α] (κCond : α → ProbabilityTheory.Kernel β Ω)
  [∀ (a : α), ProbabilityTheory.IsMarkovKernel (κCond a)]
  (h_atom : ∀ (x y : α), x ∈ measurableAtom y → κCond x = κCond y),
  ProbabilityTheory.IsMarkovKernel (ProbabilityTheory.Kernel.condKernelCountable κCond h_atom)