Complete the tree diagram:

• Probability of winning the semi-final: \( p \)
• Probability of losing the semi-final: \( 1 – p \)
• If wins semi-final, probability of winning the final: 0.6
• If wins semi-final, probability of losing the final: \( 1 – 0.6 = 0.4 \)
• If loses semi-final, no final, so probabilities are not applicable (0 for champion, 1 for not champion, but tree ends).

Probability of not being champion = \( p \cdot 0.4 + (1 – p) \cdot 1 = 0.58 \)

Solve: \( 0.4p + 1 – p = 0.58 \)

\( 1 – 0.6p = 0.58 \)

\( 0.6p = 0.42 \)

\( p = \frac{0.42}{0.6} = 0.7 \)

\(\boxed{0.7}\)

Given not champion, use conditional probability:

Total probability not champion = 0.58

Probability lose semi-final and not champion = \( (1 – p) \cdot 1 = 0.3 \) (since \( p = 0.7 \))

Probability win semi-final and lose final = \( p \cdot 0.4 = 0.7 \cdot 0.4 = 0.28 \)

Probability lose semi-final given not champion = \(\frac{0.3}{0.58} \approx 0.5172\)

\(\boxed{\frac{15}{29}}\)