I dont think there is way in the API to extract this. They allow you to control the way you sample using softmax temperatures but dont expose the probabilities directly. I resort to just empirical sampling, of course it is not efficient, but it works

def estimate_probabilities(prompt, n_samples=100):
    responses = []
    
    for _ in range(n_samples):
        response = anthropic. completions.create(
            model="<your model of choice here>",
            prompt=prompt,
            temperature=1.0,
            max_tokens_to_sample=1024
        )
        responses.append(response.content)
        time.sleep(0.1)
    
    unique_responses = set(responses)
    probabilities = {
        response: responses.count(response) / n_samples 
        for response in unique_responses
    }
    
    return dict(sorted(probabilities.items(), key=lambda x: x[1], reverse=True)

If you need cascading for many tokens in the completion like OpenAI does you will need to extend my code accordingly