Odds of Getting In
This question doesn't really lend itself to a short answer.
Let's begin with local police departments. City, town, and county leaders want their communities to be safe places to live; hence you'll find an ongoing need for police officers to staff local departments. That's good news. However, some local police departments may have limited hiring funds due to budget constraints. Not great news. However, you may still find a job because local departments may see excessive employee turnover due to comparatively low wages. Conclusion: If you're qualified, you stand a good chance of getting in. If you're a trained officer, and are laid off due to funding shortfalls, you should be able to easily find employment with another law enforcement agency.
Now let's move to state-level and federal police officer jobs. You'll find stiff competition when you play in the big leagues; mostly because larger departments and federal agencies offer better pay along with better advancement and lateral-transfer options. If you happen to be a bilingual candidate with a bachelor's degree, you have an advantage. If you can combine those attributes with prior military or law enforcement experience, especially investigative background, you'll be a sought-after commodity in federal agency employment circles.