probable cause:The amount and quality of information police must have before they can arrest or search without a warrant or that a judge must have before she will sign a search warrant allowing the police to conduct a search or arrest a suspect. Reliable information must show that it's more likely than not that a crime has occurred and the suspect is involved.

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Note added at 17 hrs (2013-09-21 14:16:02 GMT)
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I would like to add that for UK the term is reasonable grounds. This term may also be applied for US, but it is more general than probable cause (e.g., one can have reasonable grounds to arrest or to file an appeal, but probable cause would not apply to an appeal).

UK: Police and Criminal Evidence Act 1984
24 Arrest without warrant: constables(1)A constable may arrest without a warrant—
(a)anyone who is about to commit an offence;
(b)anyone who is in the act of committing an offence;
(c)anyone whom he has reasonable grounds for suspecting to be about to commit an offence;
(d)anyone whom he has reasonable grounds for suspecting to be committing an offence.
(2)If a constable has reasonable grounds for suspecting that an offence has been committed, he may arrest without a warrant anyone whom he has reasonable grounds to suspect of being guilty of it.
(3)If an offence has been committed, a constable may arrest without a warrant—
(a)anyone who is guilty of the offence;
(b)anyone whom he has reasonable grounds for suspecting to be guilty of it.
(4)But the power of summary arrest conferred by subsection (1), (2) or (3) is exercisable only if the constable has reasonable grounds for believing that for any of the reasons mentioned in subsection (5) it is necessary to arrest the person in question.
(5)The reasons are—
(a)to enable the name of the person in question to be ascertained (in the case where the constable does not know, and cannot readily ascertain, the person's name, or has reasonable grounds for doubting whether a name given by the person as his name is his real name);
(b)correspondingly as regards the person's address;
(c)to prevent the person in question—
(i)causing physical injury to himself or any other person;
(ii)suffering physical injury;
(iii)causing loss of or damage to property;
(iv)committing an offence against public decency (subject to subsection (6)); or
(v)causing an unlawful obstruction of the highway;
(d)to protect a child or other vulnerable person from the person in question;
(e)to allow the prompt and effective investigation of the offence or of the conduct of the person in question;
(f)to prevent any prosecution for the offence from being hindered by the disappearance of the person in question.
(6)Subsection (5)(c)(iv) applies only where members of the public going about their normal business cannot reasonably be expected to avoid the person in question.

US: Federal Rules of Criminal Procedure (2009)
Rule 4. Arrest Warrant or Summons on a Complaint
(a) Issuance. If the complaint or one or more affidavits filed with the complaint establish probable cause to believe that an offense has been committed and that the defendant committed it, the judge must issue an arrest warrant to an officer authorized to execute it. At the request of an attorney for the government, the judge must issue a summons, instead of a warrant, to a person authorized to serve it. A judge may issue more than one warrant or summons on the same complaint. If a defendant fails to appear in response to a summons, a judge may, and upon request of an attorney for the government must, issue a warrant.