\begin{eqnarray*}
\lefteqn{\pr{\text{students won} \mid \text{no draw}}} \hspace{0.5in} \\
	& = &	\frac{\pr{\text{students won} \cap \text{no draw}}}
			{\pr{\text{no draw}}} \\
	& = &	\frac{\pr{\{RS, SP, PR \}}}
			{\pr{\{RS, SP, PR, SR, PS, RP\}}} \\
	& = &	\frac{0.2 \cdot 0.2 + 0.7 \cdot 0.4 + 0.1 \cdot 0.4}
			{0.2 \cdot 0.2 + 0.7 \cdot 0.4 + 0.1 \cdot 0.4 +
			 0.7 \cdot 0.4 + 0.1 \cdot 0.2 + 0.2 \cdot 0.4} \\
	& = &	\frac{18}{37} \\
	& = &	0.486\ldots
\end{eqnarray*}