We've all done it one time or another. Instead of enunciating the syllables in "probably," a slurred "probly" comes out instead. Why does this happen?
It's really a question of efficiency. English words tend to have one or two syllables that are stressed. In this case, we say PRO-bab-ly, not pro-BAB-ly or pro-bab-LY. This naturally also means that the stressed syllables are more interesting and important to your production and understanding of the word than the unstressed ones.
Over time, and especially in rapid speech, people tend to reduce the contrast of the vowels in the unstressed syllables. It takes a little bit of extra effort to enunciate each syllable as clearly and distinctly as possible, and in many cases it's not worth the trouble if your listener is likely to know what you mean regardless. If you say "probably" slowly and carefully, you'll end up with something like "pro-bab-lee." But if you say it faster, that middle, unstressed vowel will start to get less distinct: "pro-buh-blee." No point in being extra careful: it's not like there are lots of other words that start with "praw" and end in "blee."
And once you've reached the stage of reducing an unstressed vowel to its less remarkable version, you might wonder whether it's worth saying it in the first place. Particularly if it's right next to another syllable that's very similar. And when you have the same syllable right beside itself in a word, it's more efficient just to say it once.
In fact, the omission of one of two consecutive identical syllables is so common in English and other languages that it has its own name: haplology (which is sometimes shortened to haplogy if you want to get self-referential about it).
Haplology is responsible for a variety of forms found in rapid speech in English: not just probly, but also libry (library), nesry (necessary), interpretive (interpretative), and others.
Haplology is also responsible for the forms of quite a few current English words whose longer forms are no longer in use at all, such as England from Engla land (originally "land of the Angles") and pierced earrings from pierced-ear earrings (earrings for pierced ears, not earrings that are themselves pierced). Other examples of modern pronunciations that came from haplology are Worchestershire, which is still spelled with two "shir"s, but pronounced closer to Worshire; pacifist, which used to be pacificist; and humbly, which used to be humblely.
So who knows? Maybe in another century or two, we'll also have completely forgotten about the longer versions of "probly" and "libry."