One partition total normalizes three explicit state weights. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
State row 1 uses its weight over Z
State 0 has weight 4 over partition total 7, giving probability 4/7.
P0=74=74
State row 2 uses its weight over Z
State 1 has weight 2 over partition total 7, giving probability 2/7.
P1=72=72
State row 3 uses its weight over Z
State 2 has weight 1 over partition total 7, giving probability 1/7.
P2=71=71
The same partition total normalizes each state
The denominator stays seven across all rows. Larger explicit weight gives the larger probability.