Step 1: Map the disease. Visceral leishmaniasis, or kala-azar, clusters in India's Gangetic eastern states where the sandfly vector flourishes. The core endemic quartet is Bihar, Jharkhand, West Bengal and Uttar Pradesh.
Step 2: Test each choice against the map. West Bengal, Bihar and Uttar Pradesh all sit firmly inside this endemic zone, so none of them can be the exception the question wants.
Step 3: Spot the outlier. Assam is the state that does not belong to this classical endemic list, so it is the correct except answer.
Step 4: Reinforce with epidemiology. The vector $Phlebotomus\ argentipes$ breeds in the moist alluvial soil of the Bihar plains, which is why the burden is so tightly bound to that corridor rather than the northeast.
\[\boxed{\text{Assam}}\]