The specific historical condition in which Stalin rose to power was the chaos and infighting that followed the Bolshevik Revolution.
Stalin rose to power gradually during the time that Lenin was running the Soviet Union. Then, once Lenin died, Stalin seized complete control of the country. This was made possible by the upheaval of the time and by the fact that the Soviet Union had no set method of deciding who would succeed Lenin. In other words, Stalin was able to rise because of the chaotic nature of the time (and because of his own political skills).
Stalin rose by using a series of bureaucratic posts to take power for himself and make people indebted to him. This was possible because the power structure of the Soviet Union was just being created and things were chaotic. Stalin used the opportunities provided by these conditions to amass power gradually until he was in a good position to openly take the top spot after Lenin died.