You need to draw a Venn diagram to see this, there will be 7 sections.

The ONLY section that doesn't win anything is

doesn't win game1 AND doesn't win game2 AND doesn't win game3

This is easily calculated as

3/4 * 7/8 * 15/16

The ONLY section that doesn't win anything is

doesn't win game1 AND doesn't win game2 AND doesn't win game3

This is easily calculated as

3/4 * 7/8 * 15/16