What are the causes of the Albanians being predominantly Muslim, while all the other countries in the Balkans predominantly Christian? They converted to Islam willingly just like the Turkic-speaking nations back then.
The fact that your starting premise is incorrect makes it a tad harder to give a quality answer, but I believe I get the gist of what you're trying to say. Still, I find it quite important to denote that Albanians were not, in fact, the only nation in the Balkans that converted to Islam under the Ottomans.
The Bosniaks also did, arguably earlier on and more enthusiastically than the Albanians, and so did many Serbs and Bulgarians (Belgrade, for example, was a Muslim majority city during the second half of the 17th century, with local populace accounting for a majority of the numbers), but their Muslim populations were expelled or converted back to Christianity once the Ottoman influence disappeared from the region, unlike the two aforementioned nations, that still retain a sense of Islamic identity to this day.
This fact is often used by chauvinists of differing motives, both locally and globally, to sort out Albanians and Bosniaks as traitors of their ancestors, but I do not think a refutation of such doggerel is relevant to this discussion, as I see nothing but mere curiosity in the way you phrased your question, so I'll move on to explaining why Islam spread and persisted in some areas of the Balkan peninsula while barely appearing in others.
I'll do my best to focus on Albania, as that is what you were looking for, but Bosnia, as a second Muslim-majority country of the area, cannot be ignored when talking about Islamization.
Now, the case of Bosnia and the case of Albania have some serious differences, notably in the local pre-Islamic beliefs, as well as the specifics of the conversion process that took place, but they are still marked by enough similarities to be observed together in order to gather a conclusion.
The common element in both cases is a lack of a strong Christian church in the area.
Let us first examine Bosnia: located at the crossroads of Catholic and Orthodox influence for centuries, and with a heretical church of its own, it simply lacked a strong religious foundation that existed in, for example, neighboring Croatia, and allowed the local populace to largely avoid conversion.
The generally wider array of jobs and offices a Muslim could hold were also a detrimental factor, but the same is true for other areas of the empire where the situation with religion wasn't as delicate.
Moving on to Albania, we come to realize that it also didn't have an official, or even a dominant church, having a large share of both Catholics (who generally settled the coast) and Orthodox Christians (who settled the central and the southern parts of the country), both of whom also retained some practices from the old pagan religions of the area.
The country also didn't have a single ruler who could claim all the territory that we know today as Albania. All of this greatly, and obviously, went in favor of the Turks, who established nominal control over the area without major problems.
Still, unlike Bosnia, a land completely under Ottoman control, Albania was somewhat autonomous in the early phase of the occupation, both because of the inaccessible terrain of its heartland, and the power of the local warlords, who retained control of their lands in exchange for paying hefty tributes to the Sultan. Around this time the first conversions to Islam started, but they were generally limited to the higher social classes, and the peasantry was almost exclusively Christian.
So, despite the fact that it lacked a solid, unitary foundation as much as Bosnia, Albania resisted a general conversion at a time when Muslims constituted a large part of the population of the peninsula. You might even say it was unusually Christian for the time (about 90% of Albanians were members of some Christian denomination at a time when only a minority of Bosnians were).
Things drastically changed after the downfall of Skanderbeg, and the Albanians, especially the Catholic North, experienced all the downsides of being a non-Muslim in the Ottoman Empire quite quickly, but the wider masses were generally firm in their Christian beliefs and wouldn't flock to Islam in larger numbers until the end of the 16th century. The conversion steadily continued through the ages, reaching its peak in mid 17th century, but not wrapping up until well into the 19th century.
The fact that Albanians started accepting the new religion a long time after the rest of the crew, explains why it is still very much present in Albania: at a time when neighboring Balkan countries were fighting the struggling empire and expelling the local and foreign Muslim populace alike, Albania was still getting Islamized.
This curious chain of events lead to Islam still prevailing in the modern Albanian society, as the pioneers of the Albanian national movement in the fin de siecle period came to see the religion as one of the natural components of the Albanian nation, and though they didn't think of Islam (or any other religion, for that matter) as a pillar of their nationhood, they didn't consider it an invasive ideology either, like the Serbs or the Greeks of the time did.
A similar evolution can be observed in the Bosniak national movement of the period, though the Bosniak revivalists of the modern era not only didn't consider Islam a foreign creed but also incorporated it in the very essence of the Bosniak identity in a way the Albanians did not.
/u/UrbisPreturbis has previously answered a similar question
/u/Chamboz has previously answered Why is Islam more common in the countries near the Adriatic Sea such as Albania, Kosovo, Bosnia-Herzegovina, etc and less common in the countries closer to Turkey like Bulgaria, Greece and Serbia? with follow-up questions too.
This question has come up many times on the subreddit.
EDIT: Fixing the links