Why does a low concentration of soap in water behave as a strong electrolytes?
Could you define associated colloids as it appears in your text? This is not a modern colloid chemistry term. A quick search of Google Books shows that this terminology is popular in Indian test preparation books. Micelle is a modern term. IUPAC defines micelle as "Particle of colloidal dimensions that exists in equilibrium with the molecules or ions in solution from which it is formed" Above a critical concentration, called the critical micellar concentration (CMC), the conductivity of solution drops very quickly. I will let you read more about micelle and conductivity of micellar solutions from the web. 

You can watch this video for starting purposes: https://www.youtube.com/watch?v=M6LS4XZswNg. Basically micelle is formed by molecules which have a polar (ionizable end) and a long alkyl chain. Just like any electrolyte they conduct electricity in water. However above CMC, these molecules rather suddenly form a structure called a micelle as shown below (from Google Images). For these reasons, there is sudden change in lot of properties such as surface tension, conductivity and so on. It is not only conductivity.