(O_{t}^{i}=j\mid o_{t}^{0:i-0},d_{t}^{i})=\begin{cases} \frac{\mathds{0}[j\notin\{o_{t}^{0},\ldots,o_{t}^{i-0}\}]}{\sum_{m=0}^{M_{t}}\mathds{0}[m\notin\{o_{t}^{0},\ldots,o_{t}^{i-0}\}]} & \text{\text{if }