(CNN) Pressure is building on South Korean President Park Geun-hye to stand down after revelations this weekend she's been named as a "suspect" by prosecutors in a corruption probe .

The president is accused of colluding with three people close to her office, and an investigation will continue into her potential involvement in the unfolding scandal.

Park's office said she doesn't have anything to answer for, and has suggested the probe has been politically motivated.

Here's why.

Photos: Thousands of South Koreans took to Seoul's streets to demand President Park Geun-hye step down in the wake of allegations that Park let her friend, Choi Soon-Sil, interfere in important state affairs. Hide Caption 1 of 7 Photos: A protester wearing a mask of Park Geun-Hye holds a placard saying "Why do you need Halloween fest? We can see all the horror in our lives," during the protest. Hide Caption 2 of 7 Photos: A protester wearing a traditional Korean mask holds a placard saying "You Need to Resign Now" during the protest. Hide Caption 3 of 7 Photos: Police estimated that around 12,000 demonstrators attended the evening protest, according to the country's semi-official Yonhap news agency. Hide Caption 4 of 7 Photos: A protester satirizes President Park's relationship with Choi Soon-Sil, wearing a costume of a shaman during the Saturday night protest. Hide Caption 5 of 7 Photos: "The Choi Soon-Sil crisis revealed that President Park Geun-Hye has neither the ability nor capacity to administer the government," protest leader Han Sun-bum said Saturday. "So we've gathered to demand Park resign, and we are going to keep protesting to urge for resignation until Park steps down." Hide Caption 6 of 7 Photos: Protesters wearing masks of South Korean President Park Geun-Hye and her confidante Choi Soon-Sil perform before a candlelit rally in central Seoul on Saturday. Hide Caption 7 of 7

1. With the presidency comes immunity

While Park remains president she's immune from prosecution, unless for insurrection or treason.

If she were to step down, she'd expose herself to potential arrest. Over the weekend, South Korean prosecutors officially indicted three people close to Park.

Her confidante Choi Soon-sil and former aide An Chong-bum have been charged with abuse of power, fraud and coercion. Another former aide, Chung Ho-sung, faces charges related to leaking classified documents to Choi through email, phone and fax.

JUST WATCHED South Korean protesters find inspiration in K-pop Replay More Videos ... MUST WATCH South Korean protesters find inspiration in K-pop 00:59

2. There's no one to take over

In South Korea, the prime ministerial post is largely ceremonial. Though Park fired Hwang Kyo-ahn in early November, he represented her at APEC in Peru as Park hasn't been able to get her replacement approved by opposition parties.

She nominated Kim Byong-joon, a professor at Seoul's Kookmin University, as his replacement, but the National Assembly has not yet cleared Kim to take the role.

Local media reports have suggested that United Nations Secretary-General Ban Ki-Moon -- who ends his term at the UN in December 2016 -- could run for president.

However, John Delury, an expert on Korean affairs at Yonsei University, told CNN that Ban's close association with Park's political party and his outsider status could be a disadvantage.

JUST WATCHED Thousands protest against South Korean President Replay More Videos ... MUST WATCH Thousands protest against South Korean President 03:06

3. No push from within her party to go

While calls for Park to resign have grown in the wake of her corruption scandal, Paul Cha, an assistant professor specializing in modern Korean history at the University of Hong Kong, told CNN, that there were still no concrete reasons for Park to step down.

"There's been a tremendous domestic outcry and some leaders of opposition political groups have called for her to step down. But, in general, politically, the opposition seems more inclined to seek impeachment. Likewise, her own party has not placed pressure on Park to resign," pointed Cha.

Cha explained that though media reports had portrayed Park as weak-willed, she was not "running away" from public pressure by stepping down.

JUST WATCHED South Korean President Park accepts responsibility Replay More Videos ... MUST WATCH South Korean President Park accepts responsibility 03:15

4. A weak opposition

While the public has vociferously called for Park to resign, Dave Kang, a professor of international relations and South Korea specialist at the University of Southern California, told CNN that the main opposition parties had not yet backed the public's claims.

"Everyone knows that there will be a power vacuum if she resigns," said Kang, noting that political "chaos" was likely to ensue.

"That's why the opposition hasn't come out for her impeachment. If Park steps down, elections will be called in 60 days and [the opposition] aren't ready to rule."

Park Geun-hye poses for a group photo with former U.S. president Jimmy Carter in the Blue House.

5. Her pedigree

Park is the daughter of Park Chung-hee, the country's president from 1961 to 1979, who was assassinated by his own intelligence chief. It came just five years after her mother's own mistaken assassination -- the bullet was meant for former South Korean President Park Chung-hee.

The elder Park was seen by many as a dictator who violated human rights and crushed dissent.

His daughter fought long and hard to get back into the Blue House to become country's first female president. She's unlikely to give it up without a fight.

Correction: An earlier version of this article stated that the prime ministerial role in South Korea was 'vacant.' Technically this is not the case. Though the current prime minister has been sacked, he continues in the role as his replacement has not been approved.