Hillel - The Oleh from Bavel

Pesachim 66a:

When Bnei Bteira didn't know if the Korban Pesach should be slaughtered on Shabbos (the halacha was hidden from them) they turned to Hillel and he answered them based on a drasha. They were so impressed they made him the Nasi. We know that the only Korban Pesach brought in the Midbar was brought on Shabbos so how did they not know?

Why was the halacha hidden from them? It was hashgacha pratis so Hillel could rise to greatness (similar to Pesach Sheni and Bnot Tzelafchad). Why did it happen that it was specifically about Korban Pesach?

Delivered at the OU Israel Center, June 18, 2019 (15 Sivan 5775)