The gemara says that when 2 eidim testify that someone is kohen, and another 2 eidim contradict them by saying that he is a chalal (born from a gerusha and therefore not a kohen), we follow chazaka. Therefore, if his father was accepted as a kohen, we assume he is also a kohen. Tosafos points out that Rashi in kiddushin holds that we don't use the chazaka of a parent for a child, but Tosafos disagrees and holds that the chazaka of the parent will work for the child, but m'drabonon we are machmir not to follow any chazaka.
However, the application of following chazaka here seems strange. Both groups of eidim admit that the father of this person is a kohen, the only point of contradiction is whether the son is a chalal. How does the chazaka of the father help resolve this question. Both witnesses agree with the fact that the father is a kohen, yet one group claims that the son isn't a kohen since his father married a gerusha. How can chazaka resolve this dispute?
This gemara sheds some insight into what chazaka does. Chazaka is a "hanhaga", meaning it is a way of behaving, rather than a "hachra'ah", meaning a determination of the halacha. From a perspective of trying to determine whether or not he is a kohen, the chazaka doesn't add any new information or rationale to assume that he is indeed a kohen. But, in the absence of any witnesses we would have said that since his father is a kohen, we entitle him to all the privileges of being a kohen. Meaning, we use the chazaka of the father not to determine that he is in fact a kohen, but to allow him to continue acting as a kohen. Therefore, when we have 2 contradictory sets of witnesses, they cancel each other out and we rely on the chazaka that the father was a kohen to allow the son to also behave like a kohen.