After the end of World War II (WWII), communism was spreading across Eastern Europe. Greece appeared to be the next in line.
In 1947, Greece pleaded for help to fight against the communists forces. To counter the communist forces, Truman set up the Truman Doctrine. The main aim of the Truman Doctrine was to contain the spread of communism without pushing it back. Also, USA would not return to isolationism like before the WWII. Under the Truman Doctrine, USA sent economic and military help to Greece and later, Turkey. USA sent about $300million worth of help to Greece and $100million worth of help to Turkey.
Probability of nuclear war was quite low, as even though USA and USSR did not like each other, USA saw no need to use nuclear weapons yet, and USSR did not possess nuclear weapons yet.