Alcoholic Ketoacidosis: This condition is likely given the patient's history of consuming alcohol for the last 3 days without eating, leading to a state where the body starts breaking down fat for energy, producing ketones. The random blood sugar (RBS) of 26 mg/dl, which is below normal, supports this diagnosis as it indicates the body's inability to utilize glucose properly, possibly due to alcohol-induced inhibition of gluconeogenesis.

Hypoglycemia due to Alcohol: Alcohol inhibits gluconeogenesis, leading to hypoglycemia, especially in a fasting state. The patient's RBS of 26 mg/dl is significantly low, supporting this diagnosis.
Dehydration and Electrolyte Imbalance: Alcohol consumption can lead to dehydration and electrolyte imbalances, which might not be directly indicated by the RBS level but are common in patients with a history of alcohol consumption without adequate nutrition and hydration.

Wernicke's Encephalopathy: Although less likely, this is a medical emergency that can occur in chronic alcoholics due to thiamine deficiency. It presents with confusion, ataxia, and ophthalmoplegia. Missing this diagnosis can lead to severe and irreversible neurological damage.
Alcoholic Hepatitis: This condition can present with hypoglycemia among other symptoms like jaundice and abdominal pain. It's crucial not to miss this diagnosis as it requires specific treatment and can have a high mortality rate if not addressed promptly.

Insulinoma or Other Endocrine Disorders: Though rare, an insulinoma (a tumor of the pancreas that produces excess insulin) could cause hypoglycemia. Other endocrine disorders affecting glucose metabolism could also be considered, albeit rarely, in the differential diagnosis of a patient presenting with hypoglycemia.
Glycogen Storage Diseases: These are rare genetic disorders that affect the body's ability to store and release glucose from glycogen. They could potentially cause hypoglycemia, especially in fasting states, but are much less likely given the patient's age and presentation.