How did Peter KNOW Corneilus and his house recieved the Holy ghost baptism?
I think we can find the answer to your question in what is said in the description of the incident, and what Peter said when he later described it to the church in Jerusalem. We can see clearly from the text how Peter knew that they had received a baptism with the Holy Spirit.
In Acts 10:44-46, the scripture says, "While Peter yet spake these words, the Holy Ghost fell on all them which heard the word. And they of the circumcision which believed were astonished, as many as came with Peter, because that on the Gentiles also was poured out the gift of the Holy Ghost. For they heard them speak with tongues, and magnify God." The passage itself says that Peter and those who were with him recognized it because they heard them speak with tongues. From Acts 8:14-18 we know that the gifts of the Holy Spirit (which, according to 1 Corinthians 12 includes speaking in tongues) were not unknown to the apostles. So how did this differ from times such as Acts 8?
In Chapter 11, Peter tells the church in Jerusalem what had happened at Cornelius house. "And as I began to speak, the Holy Ghost fell on them, as on us at the beginning. Then remembered I the word of the Lord, how that he said, John indeed baptized with water; but ye shall be baptized with the Holy Ghost. Forasmuch then as God gave them the like gift as he did unto us, who believed on the Lord Jesus Christ; what was I, that I could withstand God? (Acts 11:15-17)" Peter says he knew this to be the baptism of the Holy Spirit because it happened just the way it happened to the apostles on Pentecost. Maybe it included the noise of a wind and the tongues like fire; maybe it didn't. What it did include was the Holy Spirit coming upon the household of Cornelius and allowing them to speak in languages they had not previously learned without the apostles laying their hands on them.
Peter and the others were astonished. Why? Because this was something that had apparently never happened in the ten years since the founding of the church on the Pentecost after Jesus death. Between these two examples of the baptism of the Holy Spirit, the only way to get the gifts was, according to Acts 8:17-18, the laying on of the apostles hands. That wasnt necessary in this case. It is the only other recorded case of the baptism of the Holy Spirit. There was no need for it to happen again. It happened once to show the Jews that the apostles were selected by God to spread his word. It happened a second time to show the Gentiles were accepted in the church. Since those are the only two groups of people (Jews and everyone else), it is not likely to happen a third time.
As an aside to the matter, I believe, although there is no direct scripture to support this, that the household of Cornelius also had the power to pass on the gifts of the Holy Spirit by the laying on of their hands. The other side of the coin, though, is that as soon as the apostles and Cornelius and those present with Cornelius had all died, the power to lay hands on people to give them the gifts, and therefore the gifts themselves, ended.