The way to solve this (ignoring the problem of leap year for a moment since it won't change the answer much) is this.
It is easier to combine probabilities then to tease them apart, so we change the problem a bit. Instead of caculating the odds that two people will share a birthday, it turns out it is easier to calculate teh odds that some number of people won't share a birth day (and then just subtract from 1).
The first person has a birthday.
The second person can be born on any of the 365 days, 364 of them won't be a match, so the odds that the second person doesn't share a birthday with the first is 364/365.
The third person can be born on any of the 365 days. Of all the times the first two people have unique birthdays, so the odds of the third person having a unique birthday is 363/365. The so the total odds of 3 people having unique birthdays is 364/365 * 363/265
So the get 30 people with unique birthdays you multiply all of these probabilities together.
364/365 * 363/365 * 362/365 ..... * 335/365
This comes out to about 29.4% (which is the odds of 30 people having unique birthdays). This means the odds that two of them will share a birthday is about 70.6%.
I would say this falls short of "near certainty".