Before smoothing, a zero feature count gives an exact zero likelihood. This side example shows the raw count arithmetic that the add-one policy changes next.
highlighted = computed this step
Start from the raw zero count
Before add-one smoothing, the side feature F3 has raw count 0 inside class A and raw count 1 inside class B.
F3=1:A count 0,B count 1
Make the unsmoothed ratios
The unsmoothed likelihood for A is 0/4 = 0. For B it is 1/2 = 1/2.
P(F3=1∣A)=0/4=0,P(F3=1∣B)=1/2
A product with a zero factor is zero
An unsmoothed A product containing that zero factor becomes 0. Smoothing is a declared policy applied before scoring; this zero-count demo is exact count arithmetic only, not a claim of accuracy, calibration, or generalization, and not proof that smoothing is always better.