Sensor Markov Property

A Sensor Model has the sensor markov property iff

P(EtX0:t,E1:t1)=P(EtXt)\mathrm{P}\left(\mathrm{E}_t \mid \mathrm{X}_{0: t}, \mathrm{E}_{1: t-1}\right)=\mathrm{P}\left(\mathrm{E}_t \mid \mathrm{X}_t\right)