Firstly, I will tell about “Niyoga” and then I will come to the answer.
Niyoga is a sprocedure through which a widow can get a son by the help of a saint or Rishi and the child will be considered the son of her husband and the biological father will have no right on that. Niyog is restricted only for birth of child and not for fun. This is only for those women whoes husband was died without son. In the procedure, a saint or Rishi sees that woman from a distance and using his power of Niyoga, that woman get pregnant.
Now, coming to the story :-
Due to the untimely death of Vichitravirya, his queens Ambika and Ambalika were got the pregnancy with the Maharishi Ved Vyasa in Niyoga procedure. Ambika first mated with Vyasa through the niyoga process but kept her eyes closed during the process because his appearance and power frightened her. As a result, she gave birth to the blind Dhritarashtra. Later her sister Ambalika followed the same process with Vyasa, and knew to keep her eyes open. But she was pale with fear during the niyoga, and so gave birth to the albino (you can search about it on Google) Pandu. As both children have some abnormalities born by Ambika and Ambalika, so they sent their maiden Parishrami ( a Shudra ) in their place, who behaved appropriately during the niyoga process and gave birth to the exceptional Vidura.
Vidura’s father is Vyasa, a half-caste, and his mother a sudra maid. His status was always lower than his two half-brothers (Pandu and Dhritarashtra). That is why, Vidura is a Shudra.
