Chances are about even that Antoine is hungry. It is probable that John picked up the apple. There is almost no chance that Lily is a lion. There is almost no chance that if Antoine is hungry, and Lily is a lion, then Daniel is in the garden. It is probably the case that if Antoine is hungry, or Lily is a lion, then Jessica is a wolf. It is probably the case that if Lily is a lion, and John picked up the apple, then Mary moved to the garden.
It is certain that daniel is in the garden, and John picked up the apple.
This example is invalid.