Isn't the Passover kept in the first month? Why is this one in the second?

The Law sets it in the first month: "In the first month, on the fourteenth day of the month in the evening, is the LORD’s Passover" (Leviticus 23:5). This chapter gives its own reason for the second: "For they could not keep it at that time, because the priests had not sanctified themselves in sufficient number, and the people had not gathered themselves together to Jerusalem" (30:3). The chapter before tells that the priests and Levites "began on the first day of the first month to sanctify" the LORD's house, and that "on the sixteenth day of the first month they finished" (29:17). The Law had also given a second-month Passover, for two kinds of people: "If any man of you or of your generations is unclean by reason of a dead body, or is on a journey far away, he shall still keep the Passover to the LORD. In the second month, on the fourteenth day at evening they shall keep it" (Numbers 9:10-11). This chapter doesn't cite Numbers 9, and doesn't say whether the king had it in mind. It says the king "had taken counsel with his princes and all the assembly in Jerusalem to keep the Passover in the second month" (30:2), and "The thing was right in the eyes of the king and of all the assembly" (30:4). They killed it "on the fourteenth day of the second month" (30:15).