Immobilization or Stasis Dermatitis: This is a common condition that occurs due to prolonged immobilization, leading to increased venous pressure and subsequent petechial rash on the lower legs. The justification for this being the most likely diagnosis is the high prevalence of mobility issues in various populations and the direct mechanical effect of stasis on blood vessels.

Vitamin Deficiencies (Vitamin C or K): Deficiencies in these vitamins can lead to impaired collagen synthesis and blood clotting, respectively, which may manifest as petechiae. This is a likely diagnosis due to the relatively common occurrence of nutritional deficiencies.
Medication Side Effects (e.g., anticoagulants, steroids): Certain medications can increase the risk of bleeding or affect blood vessel integrity, leading to petechial rashes. This is a plausible diagnosis given the widespread use of such medications.
Infections (e.g., viral, bacterial): Some infections can cause petechial rashes, either through direct invasion of the skin or through immune-mediated mechanisms. This is a likely diagnosis due to the frequency of infectious diseases.

Meningococcemia: Although less common, this condition is life-threatening and can present with a petechial rash. Early recognition is crucial for survival, making it a "do not miss" diagnosis.
Disseminated Intravascular Coagulation (DIC): This is a serious disorder in which the proteins responsible for blood clotting become overactive, leading to widespread clotting and bleeding, including petechiae. The severity and potential for high mortality rate make it critical not to miss.
Thrombocytopenia or Thrombocytopathia: Conditions affecting platelet count or function can lead to petechial rashes due to impaired blood clotting. These conditions can be due to various causes, including autoimmune diseases, medications, or bone marrow disorders, and are critical to identify due to their potential impact on patient management and outcome.

Henoch-Schönlein Purpura (HSP): A form of vasculitis that affects blood vessels and is characterized by a purpuric rash, which can sometimes appear petechial. It's more common in children but can occur in adults, making it a rare but important consideration in the differential diagnosis of petechial rashes.
Amyloidosis: A condition characterized by the deposition of amyloid proteins in various tissues, which can lead to petechiae among other symptoms. It's rare and diagnosis often requires biopsy, but it's an important consideration in patients with unexplained petechial rashes and other systemic symptoms.
Ehlers-Danlos Syndrome: A group of disorders that affect connective tissues supporting the skin, bones, blood vessels, and many other organs and tissues. Some types can lead to easy bruising and petechiae due to fragile blood vessels. This is a rare diagnosis but important to consider in patients with a history of easy bruising, poor wound healing, and other features of connective tissue disorders.