**Core Concept**
Degenerative disc disease (DDD) is a common condition characterized by wear and tear of the intervertebral discs in the spine, leading to chronic back pain. This condition is often associated with aging and can be exacerbated by factors such as obesity, smoking, and heavy physical activity.

**Why the Correct Answer is Right**
The most probable diagnosis in this case is degenerative disc disease due to the patient's age (65 years) and symptom of chronic backache. Degenerative disc disease is a common cause of back pain in older adults, and it is often confirmed by radiographic findings such as loss of disc height, endplate sclerosis, and facet joint osteoarthritis. As people age, the discs in the spine undergo natural degeneration, leading to a loss of cushioning and increased friction between the vertebrae, resulting in pain and stiffness.

**Why Each Wrong Option is Incorrect**
**Option A:** Osteoporosis is a condition characterized by a decrease in bone density, leading to an increased risk of fractures. While osteoporosis can cause back pain, it is not the most probable diagnosis in this case, as there is no mention of a recent fall or fracture.

**Option B:** Spondylolisthesis is a condition where one vertebra slips forward over the vertebra below it, often causing back pain and stiffness. However, this condition is less common than degenerative disc disease and typically requires additional symptoms such as neurological deficits or a history of trauma.

**Option C:** Scoliosis is a condition characterized by an abnormal curvature of the spine. While scoliosis can cause back pain, it is typically diagnosed at a younger age and is not as common in older adults.

**Option D:** Osteoarthritis of the facet joints is a common cause of back pain, but it is not as prevalent as degenerative disc disease in older adults.

**Clinical Pearl / High-Yield Fact**
A key point to remember is that degenerative disc disease is a common cause of back pain in older adults, and a thorough history and physical examination should be performed to rule out other potential causes.

**Correct Answer:** C.