**Core Concept**
The question is testing the student's knowledge of sexually transmitted infections (STIs), specifically the clinical presentation and diagnosis of a common STI. The underlying principle is the identification of a specific STI based on its characteristic presentation and epidemiology.

**Why the Correct Answer is Right**
The correct answer is likely **Syphilis** (Treponema pallidum). The patient's symptom of painless penile ulcers 9 days after sexual intercourse with a professional sex worker is highly suggestive of primary syphilis. The incubation period of syphilis typically ranges from 9-90 days, with an average of 21 days. The painless nature of the ulcers is a key distinguishing feature from other STIs such as herpes simplex virus (HSV), which typically presents with painful vesicles.

**Why Each Wrong Option is Incorrect**
* **Option A:** Chancroid (Haemophilus ducreyi) typically presents with painful genital ulcers, which does not match the patient's symptom.
* **Option B:** Herpes simplex virus (HSV) typically presents with painful vesicles or ulcers, which does not match the patient's symptom.
* **Option C:** Lymphogranuloma venereum (LGV) typically presents with a painless papule or pustule, which may progress to a lymphadenopathy, but the primary lesion is often not visible.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that the presence of painless genital ulcers should raise suspicion for syphilis, especially in the context of recent sexual exposure.

**Correct Answer:** C.