We calculate partial probabilities as :
t ( j )= Pr( observation | hidden state is j ) x Pr(all paths
to state j at time t)

In the special case where t = 1, there are no paths to the
state. The probability of being in a state at t = 1 is therefore
the initial probability, i.e. Pr( state | t = 1) = (state), and we
therefore calculate partial probabilities at t = 1 as this
probability multiplied by the associated observation
probability;