According to Kohlrausch's law of independent migration of ions, "at infinite dilution when the dissociation is complete, each ion makes a definite contribution towards molar conductivity of the electrolyte, irrespective of the nature of the other ion with which it is associated."
e.g., For NaCI
∧0NaCl=λ0Na++λ0Cl−
Conductivity is the conductance of one centimetre cube of the solution. Upon diluting the solution, the concentration of ions per centimetre cube decreases and, therefore, the conductivity decreases.