**Core Concept**
The patient's symptoms, including colicky abdominal pain, distension, and hyperperistaltic abdominal sounds, along with air in the biliary tree, suggest a condition where there is a mechanical obstruction of the bile ducts, leading to bile duct dilatation and subsequent air entry into the biliary tree.

**Why the Correct Answer is Right**
The likely diagnosis is a gallstone causing a mechanical obstruction of the common bile duct, leading to bile duct dilatation and subsequent air entry into the biliary tree through the cystic duct or a patent sphincter of Oddi. This condition is known as Mirizzi's syndrome or a cholangiocholecystic fistula. The presence of colicky abdominal pain and hyperperistaltic abdominal sounds indicates that the patient is experiencing biliary colic due to the obstruction.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option might suggest a diagnosis of emphysematous cholecystitis, which is a serious condition where gas is present in the gallbladder wall, often due to gangrene or necrosis. However, the presence of air in the biliary tree is a more characteristic feature of Mirizzi's syndrome.
* **Option B:** This option might suggest a diagnosis of acute cholecystitis, which is inflammation of the gallbladder. While this condition can cause colicky abdominal pain and distension, it typically does not involve air in the biliary tree.
* **Option C:** This option might suggest a diagnosis of ascending cholangitis, which is an infection of the bile ducts. While this condition can cause colicky abdominal pain, distension, and hyperperistaltic abdominal sounds, it typically does not involve air in the biliary tree.
* **Option D:** This option might suggest a diagnosis of small bowel obstruction, which can cause colicky abdominal pain and distension. However, the presence of air in the biliary tree is a more characteristic feature of Mirizzi's syndrome.

**Clinical Pearl / High-Yield Fact**
Remember that the presence of air in the biliary tree, along with colicky abdominal pain and distension, should raise suspicion for Mirizzi's syndrome, a mechanical obstruction of the common bile duct caused by a gallstone.

**Correct Answer:** C.