While it was never explicitly stated (to my knowledge) why they discounted the possibility of a 3rd Kira, I can come up with some educated guesses.
First, there was no evidence of a 3rd person acting as Kira while the first two were active.
Remember that the investigation started by looking into a single Kira. The second Kira was discovered when Misa sent the video broadcasts as a way to contact the first Kira. It was also further cemented that the second Kira was different from the first in the way they acted. The second acted more recklessly (with less well thought out and deliberate actions), killed people that the original Kira would not have and was also shown to be able to kill without a name. The only way they found out there was a second Kira is because the evidence showed there were two people independently acting as Kira at the same time.
The "3rd Kira" (Higuchi) acted in the same way as the first Kira. This was intentional. Light wanted to use this to alleviate suspicion that he was Kira. By having Higuchi act the same way, there was no reason to believe that he wasn't the original Kira. Meaning that when Higuchi was caught, Light should be (theoretically) cleared.
Second, L already had a plethora of evidence that implicated Light as Kira. As far as L was concerned, Light was Kira. He just needed a few more details (how Light was killing people, for instance) before he could arrest Light.
Then Light comes up with the prison scheme. L is immediately suspicious. Light was trying hard, almost too hard, to prove his innocence. And L obviously couldn't take any evidence Light offered at face value. So even while Light was in prison, L was working on the assumption that Light was Kira. And when Light's personality underwent a drastic change when he gave up the notebook, it threw a wrench in L's theory. Light when from a calm denial of being Kira to having a fanatical, emotional denial. This evidence contradicted the Light-is-Kira theory.
L is now stuck between a rock and a hard place. On the one hand, everything points to Light being Kira. On the other, Light's behavior along with the continued killings seemed to exonerate Light. And since the behavior change coincided nicely with the killings resuming, the idea of the power transfer was born. And given that theory, why investigate a 3rd Kira that may not exist (and of which there was little if any evidence of)?
Third, let's play devil's advocate and assume L considered that there was a third Kira. How did this person get in contact with the first two Kiras? As far as the task force knew, there would be no special way for one Kira to find another (as evidenced by the second Kira needing to send the broadcasts to locate the original). Also, how did they communicate and coordinate with Light and Misa? Light and Misa had been under surveillance for quite a while. Surely something would have come up that would have raised a few eyebrows, especially given the nature of Misa's messages when trying to find Light? Additionally, if there was a third Kira, why did he show up now? Why would he just resume what Kira was doing without making any changes? (Remember that the connection between Kira (Higuchi) and the Yotsuba group hadn't been discovered yet.) Every person is different (especially in their values, thinking and reasoning), so there should be at least some subtle differences between two Kiras. And none of that showed up (yet).
Given all of this, there was no reason to assume a third Kira existed. Investigating every anomaly by assuming it was a separate person would have led L on a hundred wild goose chases. L was the best detective in the world. His experience and knowledge would tell him that something else was going on. Given that he knew Light and how smart Light was, he could very easily presume that every inconsistency could be Light's doing. And until proven otherwise, that's what L did. You don't throw out everything you know to be true because the accused offers an (unverified) piece of evidence of their innocence. And given the mystic powers of Kira, anything was possible, and equally difficult to verify as being impossible.
