When a probe is converted into an orbiter or lander, it immediately stops counting against the player's probe limit as soon as it is placed on the planetary board.

This is supported by the following rule:

• On page 10, under ORBIT A PLANET:
  "Once your figure is on the planetary board, it no longer counts against your limit of 'probes in space'."

• On page 8, under LAUNCH A PROBE:
  "By default, each player is limited to having one probe in space. If you are at your probe limit, you cannot take the Launch action. ('In space' is anywhere in the rings of the solar system board. By contrast, figures on the planetary board are not 'probes in space.')"

Therefore, as soon as the probe is removed from the solar system board and placed on the planetary board (as an orbiter or lander), it no longer counts toward the probe limit.

Source:
Page 10 (ORBIT A PLANET), Page 8 (LAUNCH A PROBE)

Source: Core Rulebook (pp. 10, 11, 17, 28, 8)