 This is the numerator we are looking for in our equation, and we divide by the total probability of the observation sequence to normalize this value and extract only the probability that formula_42.These values are sometimes called the "smoothed values" as they combine the forward and backward probabilities to compute a final probability.The values formula_54 thus provide the probability of being in each state at time t. As such, they are useful for determining the most probable state at any time.