What do the terms "tarjeeh" (giving preference) and "shakk ma'a al-taharri" (doubt with investigation) mean in the context of the prostration of forgetfulness?

The Fiqh Encyclopedia states that "shakk" (doubt), linguistically, is the opposite of "yaqeen" (certainty). Terminologically, it is the absence of certainty, regardless of whether the two possibilities are equal or one is more probable. "Tarjeeh" (preferring) is to give precedence to one evidence over another that contradicts it. "Taharri" (investigation/seeking accuracy), linguistically, is intention and seeking. Terminologically, it is exerting effort to achieve the intended goal or acting upon predominant conjecture when certainty is absent.

In the chapter of Sujud (definition) al-Sahw (prostration of forgetfulness), scholars differed on the meaning of "taharri": Is it acting upon certainty or upon predominant conjecture? - If "taharri" means acting upon certainty, then one builds upon the lesser number when in doubt. - If "taharri" means acting upon predominant conjecture, then the worshiper acts upon what has become preponderant to them. Example: One who doubts between three or four rak'ahs, and four becomes preponderant to them: - According to the first view (acting upon certainty), they build upon three rak'ahs and add one rak'ah. - According to the second view (acting upon predominant conjecture), they build upon four rak'ahs and add nothing. It becomes clear from the above that "taharri" in the sense of acting upon predominant conjecture and "tarjeeh" (preferring) are the same.